diff --git a/psydac/api/ast/tests/poisson.py b/psydac/api/ast/tests/poisson.py
index b5a418d37..d669986c0 100644
--- a/psydac/api/ast/tests/poisson.py
+++ b/psydac/api/ast/tests/poisson.py
@@ -1,19 +1,18 @@
 # -*- coding: UTF-8 -*-
-
+import os
 
 from sympy import symbols
-from sympy import sin,pi
+from sympy import sin, pi
 
 from sympde.calculus import grad, dot
-
 from sympde.topology import ScalarFunctionSpace
-from sympde.topology import elements_of,LogicalExpr
+from sympde.topology import elements_of, LogicalExpr
 from sympde.topology import Square
-from sympde.topology import IdentityMapping,Mapping ,PolarMapping
+from sympde.topology import Mapping, IdentityMapping, PolarMapping
 from sympde.expr     import integral
 from sympde.expr     import LinearForm
 from sympde.expr     import BilinearForm
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr.evaluation import TerminalExpr
 
 from psydac.api.ast.fem          import AST
@@ -21,7 +20,6 @@
 from psydac.api.discretization   import discretize
 from psydac.api.printing.pycode  import pycode
 
-import os
 # ...
 try:
     mesh_dir = os.environ['PSYDAC_MESH_DIR']
@@ -32,6 +30,7 @@
     mesh_dir = os.path.join(base_dir, 'mesh')
     filename = os.path.join(mesh_dir, 'identity_2d.h5')
 
+
 def test_codegen():
     domain  = Square()
     M       = Mapping('M',2)
@@ -51,22 +50,22 @@ def test_codegen():
     Vh = discretize(V, domain_h)
 
     error  = u - sin(pi*x)*sin(pi*y)
-    l2norm = LogicalExpr(M, Norm(error, domain, kind='l2'))
-    h1norm = LogicalExpr(M, Norm(error, domain, kind='h1'))
+    l2norm = LogicalExpr(M,     Norm(error, domain, kind='l2'))
+    h1norm = LogicalExpr(M, SemiNorm(error, domain, kind='h1'))
 
     ast_b = AST(b, TerminalExpr(b)[0],[Vh, Vh])
-    ast_b = parse(ast_b.expr, settings={'dim':2,'nderiv':1,'mapping':M,'target':domain.logical_domain})
+    ast_b = parse(ast_b.expr, settings={'dim':2, 'nderiv':1, 'mapping':M, 'target':domain.logical_domain})
     print(pycode(ast_b))
 
     print('==============================================================================================================')
     ast_l = AST(l, TerminalExpr(l)[0], Vh)
-    ast_l = parse(ast_l.expr, settings={'dim':2,'nderiv':1,'mapping':M,'target':domain.logical_domain})
+    ast_l = parse(ast_l.expr, settings={'dim':2, 'nderiv':1, 'mapping':M, 'target':domain.logical_domain})
     print(pycode(ast_l))
 
 
     print('==============================================================================================================')
     ast_l2norm = AST(l2norm, TerminalExpr(l2norm)[0], Vh)
-    ast_l2norm = parse(ast_l2norm.expr, settings={'dim':2,'nderiv':1,'mapping':M, 'target':domain.logical_domain})
+    ast_l2norm = parse(ast_l2norm.expr, settings={'dim':2, 'nderiv':1, 'mapping':M, 'target':domain.logical_domain})
     print(pycode(ast_l2norm))
-test_codegen()
 
+test_codegen()
diff --git a/psydac/api/ast/tests/system_1.py b/psydac/api/ast/tests/system_1.py
index 5789e625f..8f9433b1c 100644
--- a/psydac/api/ast/tests/system_1.py
+++ b/psydac/api/ast/tests/system_1.py
@@ -1,4 +1,5 @@
 # -*- coding: UTF-8 -*-
+import os
 
 from sympy import pi, sin, Tuple, Matrix
 
@@ -10,8 +11,7 @@
 from sympde.expr     import integral
 from sympde.expr     import LinearForm
 from sympde.expr     import BilinearForm
-from sympde.expr     import Norm
-
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr.evaluation import TerminalExpr
 
 from psydac.api.ast.fem          import AST
@@ -20,7 +20,6 @@
 from psydac.api.printing.pycode  import pycode
 
 
-import os
 # ...
 try:
     mesh_dir = os.environ['PSYDAC_MESH_DIR']
@@ -39,7 +38,7 @@ def test_codegen():
 
     x,y = domain.coordinates
 
-    f   = Tuple(2*pi**2*sin(pi*x)*sin(pi*y),
+    f = Tuple(2*pi**2*sin(pi*x)*sin(pi*y),
               2*pi**2*sin(pi*x)*sin(pi*y))
 
     Fe = Tuple(sin(pi*x)*sin(pi*y), sin(pi*x)*sin(pi*y))
@@ -50,12 +49,12 @@ def test_codegen():
 
     int_0 = lambda expr: integral(domain , expr)
 
-    b = BilinearForm((u,v), int_0(inner(grad(v), grad(u))))
+    b = BilinearForm((u, v), int_0(inner(grad(v), grad(u))))
     l = LinearForm(v, int_0(dot(f, v)))
 
     error = Matrix([F[0]-Fe[0], F[1]-Fe[1]])
-    l2norm_F = Norm(error, domain, kind='l2')
-    h1norm_F = Norm(error, domain, kind='h1')
+    l2norm_F =     Norm(error, domain, kind='l2')
+    h1norm_F = SemiNorm(error, domain, kind='h1')
 
     # Create computational domain from topological domain
     domain_h = discretize(domain, filename=filename)
@@ -64,17 +63,16 @@ def test_codegen():
     Vh = discretize(V, domain_h)
 
     print('============================================BilinearForm=========================================')
-    ast_b    = AST(b, TerminalExpr(b)[0], [Vh, Vh])
-    stmt_b = parse(ast_b.expr, settings={'dim':2,'nderiv':1, 'mapping':Vh.symbolic_mapping})
+    ast_b  = AST(b, TerminalExpr(b)[0], [Vh, Vh])
+    stmt_b = parse(ast_b.expr, settings={'dim':2, 'nderiv':1, 'mapping':Vh.symbolic_mapping})
     print(pycode(stmt_b))
 
     print('============================================LinearForm===========================================')
-    ast_l    = AST(l, TerminalExpr(l)[0], Vh)
-    stmt_l = parse(ast_l.expr, settings={'dim':2,'nderiv':1, 'mapping':Vh.symbolic_mapping})
+    ast_l  = AST(l, TerminalExpr(l)[0], Vh)
+    stmt_l = parse(ast_l.expr, settings={'dim':2, 'nderiv':1, 'mapping':Vh.symbolic_mapping})
     print(pycode(stmt_l))
 
-    print('============================================Norm===========================================')
+    print('============================================SemiNorm===========================================')
     ast_norm = AST(h1norm_F, TerminalExpr(h1norm_F)[0], Vh)
-    stmt_n = parse(ast_norm.expr, settings={'dim':2,'nderiv':1, 'mapping':Vh.symbolic_mapping})
+    stmt_n = parse(ast_norm.expr, settings={'dim':2, 'nderiv':1, 'mapping':Vh.symbolic_mapping})
     print(pycode(stmt_n))
-
diff --git a/psydac/api/discretization.py b/psydac/api/discretization.py
index accb814c0..e097d4621 100644
--- a/psydac/api/discretization.py
+++ b/psydac/api/discretization.py
@@ -3,6 +3,7 @@
 # TODO: - init_fem is called whenever we call discretize. we should check that
 #         nderiv has not been changed. shall we add nquads too?
 import os
+
 from sympy import Expr as sym_Expr
 import numpy as np
 
@@ -11,7 +12,7 @@
 from sympde.expr     import LinearForm as sym_LinearForm
 from sympde.expr     import Functional as sym_Functional
 from sympde.expr     import Equation as sym_Equation
-from sympde.expr     import Norm as sym_Norm
+from sympde.expr     import Norm as sym_Norm, SemiNorm as sym_SemiNorm
 from sympde.expr     import TerminalExpr
 
 from sympde.topology import BasicFunctionSpace
@@ -39,9 +40,8 @@
 from psydac.fem.vector       import ProductFemSpace, VectorFemSpace
 from psydac.cad.geometry     import Geometry
 from psydac.mapping.discrete import NurbsMapping
-
-from psydac.linalg.stencil     import StencilVectorSpace
-from psydac.linalg.block       import BlockVectorSpace
+from psydac.linalg.stencil   import StencilVectorSpace
+from psydac.linalg.block     import BlockVectorSpace
 
 __all__ = ('discretize', 'discretize_derham', 'reduce_space_degrees', 'discretize_space', 'discretize_domain')
 
@@ -445,7 +445,7 @@ def discretize(a, *args, **kwargs):
         kwargs['symbolic_mapping'] = mapping
 
     if isinstance(a, sym_BasicForm):
-        if isinstance(a, sym_Norm):
+        if isinstance(a, (sym_Norm, sym_SemiNorm)):
             kernel_expr = TerminalExpr(a, domain)
             if not mapping is None:
                 kernel_expr = tuple(LogicalExpr(i, domain) for i in kernel_expr)
diff --git a/psydac/api/fem.py b/psydac/api/fem.py
index 8cb856a55..098b80904 100644
--- a/psydac/api/fem.py
+++ b/psydac/api/fem.py
@@ -10,6 +10,7 @@
 from sympde.expr          import LinearForm as sym_LinearForm
 from sympde.expr          import Functional as sym_Functional
 from sympde.expr          import Norm as sym_Norm
+from sympde.expr          import SemiNorm as sym_SemiNorm
 from sympde.topology      import Boundary, Interface
 from sympde.topology      import VectorFunctionSpace
 from sympde.topology      import ProductSpace
@@ -1525,7 +1526,7 @@ def assemble(self, **kwargs):
 
         Example
         --------------
-        n = Norm(1.0j*v, domain, kind='l2')
+        n = SemiNorm(1.0j*v, domain, kind='l2')
         nh = discretize(n, domain_h,      Vh , **kwargs)
         fh = FemField(Vh)
         fh.coeffs[:] = 1
@@ -1555,7 +1556,7 @@ def assemble(self, **kwargs):
                 args += (v, )
 
         v = self._func(*args)
-        if isinstance(self.expr, sym_Norm):
+        if isinstance(self.expr, (sym_Norm, sym_SemiNorm)):
             if not( self.comm is None ):
                 v = self.comm.allreduce(sendobj=v)
 
diff --git a/psydac/api/tests/test_2d_biharmonic.py b/psydac/api/tests/test_2d_biharmonic.py
index fe259a06f..7a15bd7c3 100644
--- a/psydac/api/tests/test_2d_biharmonic.py
+++ b/psydac/api/tests/test_2d_biharmonic.py
@@ -13,7 +13,7 @@
 from sympde.topology import Square
 from sympde.topology import Union
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -74,9 +74,9 @@ def run_biharmonic_2d_dir(solution, f, dir_zero_boundary, ncells, degree, backen
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
-    h2norm = Norm(error, domain, kind='h2')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
+    h2norm = SemiNorm(error, domain, kind='h2')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_2d_complex.py b/psydac/api/tests/test_2d_complex.py
index e678471c4..57e6a37db 100644
--- a/psydac/api/tests/test_2d_complex.py
+++ b/psydac/api/tests/test_2d_complex.py
@@ -17,7 +17,7 @@
 from sympde.topology import Domain, Square
 from sympde.topology import IdentityMapping, AffineMapping, PolarMapping
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -87,9 +87,9 @@ def run_biharmonic_2d_dir(solution, f, dir_zero_boundary, ncells=None, degree=No
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
-    h2norm = Norm(error, domain, kind='h2')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
+    h2norm = SemiNorm(error, domain, kind='h2')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
@@ -170,8 +170,8 @@ def run_poisson_2d(solution, f, domain, ncells=None, degree=None, filename=None,
 
     equation = find(u, forall=v, lhs=1j*a(u,v), rhs=1j*l(v), bc=bc)
 
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
@@ -223,8 +223,8 @@ def run_helmholtz_2d(solution, kappa, e_w_0, dx_e_w_0, domain, ncells=None, degr
 
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v))
 
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_2d_laplace.py b/psydac/api/tests/test_2d_laplace.py
index b59cdcc1d..1a7b781e3 100644
--- a/psydac/api/tests/test_2d_laplace.py
+++ b/psydac/api/tests/test_2d_laplace.py
@@ -13,7 +13,7 @@
 from sympde.topology import Square
 from sympde.topology import Union
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -78,8 +78,8 @@ def run_laplace_2d(solution, f, dir_zero_boundary, dir_nonzero_boundary,
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_2d_mapping_biharmonic.py b/psydac/api/tests/test_2d_mapping_biharmonic.py
index cb5e9ebae..cd4df2c3e 100644
--- a/psydac/api/tests/test_2d_mapping_biharmonic.py
+++ b/psydac/api/tests/test_2d_mapping_biharmonic.py
@@ -29,7 +29,7 @@
 from sympde.topology import Domain,Square
 from sympde.topology import Union
 from sympde.expr import BilinearForm, LinearForm, integral
-from sympde.expr import Norm
+from sympde.expr import Norm, SemiNorm
 from sympde.expr import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -100,9 +100,9 @@ def run_biharmonic_2d_dir(filename, solution, f, dir_zero_boundary,
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
-    h2norm = Norm(error, domain, kind='h2')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
+    h2norm = SemiNorm(error, domain, kind='h2')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_2d_mapping_laplace.py b/psydac/api/tests/test_2d_mapping_laplace.py
index 7b0b3d529..616bcf6b6 100644
--- a/psydac/api/tests/test_2d_mapping_laplace.py
+++ b/psydac/api/tests/test_2d_mapping_laplace.py
@@ -29,7 +29,7 @@
 from sympde.topology import Domain,Square
 from sympde.topology import Union
 from sympde.expr import BilinearForm, LinearForm, integral
-from sympde.expr import Norm
+from sympde.expr import Norm, SemiNorm
 from sympde.expr import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -101,8 +101,8 @@ def run_laplace_2d(filename, solution, f, dir_zero_boundary,
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_2d_mapping_poisson.py b/psydac/api/tests/test_2d_mapping_poisson.py
index ed9f3c0a6..ab734f451 100644
--- a/psydac/api/tests/test_2d_mapping_poisson.py
+++ b/psydac/api/tests/test_2d_mapping_poisson.py
@@ -29,7 +29,7 @@
 from sympde.topology import Domain
 from sympde.topology import Union
 from sympde.expr import BilinearForm, LinearForm, integral
-from sympde.expr import Norm
+from sympde.expr import Norm, SemiNorm
 from sympde.expr import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -106,8 +106,8 @@ def run_poisson_2d(filename, solution, f, dir_zero_boundary,
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_2d_multipatch_mapping_poisson.py b/psydac/api/tests/test_2d_multipatch_mapping_poisson.py
index 5b32bd1fa..1c9677e2d 100644
--- a/psydac/api/tests/test_2d_multipatch_mapping_poisson.py
+++ b/psydac/api/tests/test_2d_multipatch_mapping_poisson.py
@@ -16,7 +16,7 @@
 from sympde.topology      import IdentityMapping, PolarMapping, AffineMapping
 from sympde.expr.expr     import LinearForm, BilinearForm
 from sympde.expr.expr     import integral
-from sympde.expr.expr     import Norm
+from sympde.expr.expr     import Norm, SemiNorm
 from sympde.expr.equation import find, EssentialBC
 
 from psydac.api.discretization     import discretize
@@ -76,8 +76,8 @@ def run_poisson_2d(solution, f, domain, ncells=None, degree=None, filename=None,
 
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v))
 
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_2d_multipatch_poisson.py b/psydac/api/tests/test_2d_multipatch_poisson.py
index d8b276403..2ecf457ac 100644
--- a/psydac/api/tests/test_2d_multipatch_poisson.py
+++ b/psydac/api/tests/test_2d_multipatch_poisson.py
@@ -11,7 +11,7 @@
 from sympde.topology      import IdentityMapping, AffineMapping
 from sympde.expr.expr     import LinearForm, BilinearForm
 from sympde.expr.expr     import integral
-from sympde.expr.expr     import Norm
+from sympde.expr.expr     import Norm, SemiNorm
 from sympde.expr.equation import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -53,8 +53,8 @@ def run_poisson_2d(solution, f, domain, ncells, degree):
 
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
 
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_2d_navier_stokes.py b/psydac/api/tests/test_2d_navier_stokes.py
index 296caf612..992b9dbdc 100644
--- a/psydac/api/tests/test_2d_navier_stokes.py
+++ b/psydac/api/tests/test_2d_navier_stokes.py
@@ -126,7 +126,7 @@ def run_time_dependent_navier_stokes_2d(filename, dt_h, nt, newton_tol=1e-4, max
 
     # Define (abstract) norms
     l2norm_du  = Norm(Matrix([du[0],du[1]]), domain, kind='l2')
-    l2norm_dp  = Norm(dp     , domain, kind='l2')
+    l2norm_dp  = Norm(dp, domain, kind='l2')
 
     # ... create the computational domain from a topological domain
     domain_h = discretize(domain, filename=filename)
@@ -262,11 +262,11 @@ def run_steady_state_navier_stokes_2d(domain, f, ue, pe, *, ncells, degree, mult
     equation = find((du, dp), forall=(v, q), lhs=a((du, dp), (v, q)), rhs=l(v, q), bc=bc)
 
     # Define (abstract) norms
-    l2norm_u   = Norm(Matrix([u[0]-ue[0],u[1]-ue[1]]), domain, kind='l2')
-    l2norm_p   = Norm(p-pe  , domain, kind='l2')
+    l2norm_u   = Norm(Matrix([u[0]-ue[0], u[1]-ue[1]]), domain, kind='l2')
+    l2norm_p   = Norm(p - pe, domain, kind='l2')
 
     l2norm_du  = Norm(Matrix([du[0],du[1]]), domain, kind='l2')
-    l2norm_dp  = Norm(dp     , domain, kind='l2')
+    l2norm_dp  = Norm(dp, domain, kind='l2')
 
     # ... create the computational domain from a topological domain
     domain_h = discretize(domain, ncells=ncells, comm=comm)
diff --git a/psydac/api/tests/test_2d_poisson.py b/psydac/api/tests/test_2d_poisson.py
index 100db499f..ec3afd18a 100644
--- a/psydac/api/tests/test_2d_poisson.py
+++ b/psydac/api/tests/test_2d_poisson.py
@@ -13,7 +13,7 @@
 from sympde.topology import Square
 from sympde.topology import Union
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -83,8 +83,8 @@ def run_poisson_2d(solution, f, dir_zero_boundary, dir_nonzero_boundary,
 
     # Error norms
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_api_2d_fields.py b/psydac/api/tests/test_api_2d_fields.py
index 54c0989f2..9946af354 100644
--- a/psydac/api/tests/test_api_2d_fields.py
+++ b/psydac/api/tests/test_api_2d_fields.py
@@ -355,4 +355,4 @@ def teardown_module():
 
 def teardown_function():
     from sympy.core import cache
-    cache.clear_cache()
\ No newline at end of file
+    cache.clear_cache()
diff --git a/psydac/api/tests/test_api_2d_scalar_analytical_mapping.py b/psydac/api/tests/test_api_2d_scalar_analytical_mapping.py
index 4da037c3b..98efa61f7 100644
--- a/psydac/api/tests/test_api_2d_scalar_analytical_mapping.py
+++ b/psydac/api/tests/test_api_2d_scalar_analytical_mapping.py
@@ -8,7 +8,7 @@
 from sympde.topology      import PolarMapping
 from sympde.expr.expr     import LinearForm, BilinearForm
 from sympde.expr.expr     import integral
-from sympde.expr.expr     import Norm
+from sympde.expr.expr     import Norm, SemiNorm
 from sympde.expr.equation import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -33,8 +33,8 @@ def run_poisson_2d(solution, f, domain, ncells, degree, comm=None):
 
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
 
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     #+++++++++++++++++++++++++++++++
     # 2. Discretization
diff --git a/psydac/api/tests/test_api_2d_system.py b/psydac/api/tests/test_api_2d_system.py
index c98043125..a1bc48c38 100644
--- a/psydac/api/tests/test_api_2d_system.py
+++ b/psydac/api/tests/test_api_2d_system.py
@@ -11,7 +11,7 @@
 from sympde.topology import element_of
 from sympde.topology import Square
 from sympde.expr import BilinearForm, LinearForm, integral
-from sympde.expr import Norm
+from sympde.expr import Norm, SemiNorm
 from sympde.expr import find, EssentialBC
 
 from psydac.fem.basic          import FemField
@@ -49,12 +49,12 @@ def run_system_1_2d_dir(Fe, Ge, f0, f1, ncells, degree):
     l  = LinearForm((v,q), l0(v) + l1(q))
 
     error = Matrix([F[0]-Fe[0], F[1]-Fe[1]])
-    l2norm_F = Norm(error, domain, kind='l2')
-    h1norm_F = Norm(error, domain, kind='h1')
+    l2norm_F =     Norm(error, domain, kind='l2')
+    h1norm_F = SemiNorm(error, domain, kind='h1')
 
     error = G-Ge
-    l2norm_G = Norm(error, domain, kind='l2')
-    h1norm_G = Norm(error, domain, kind='h1')
+    l2norm_G =     Norm(error, domain, kind='l2')
+    h1norm_G = SemiNorm(error, domain, kind='h1')
 
     bc = EssentialBC(u, 0, domain.boundary)
     equation = find([u,p], forall=[v,q], lhs=a((u,p),(v,q)), rhs=l(v,q), bc=bc)
diff --git a/psydac/api/tests/test_api_2d_vector.py b/psydac/api/tests/test_api_2d_vector.py
index 6f9e1163c..7b8449b87 100644
--- a/psydac/api/tests/test_api_2d_vector.py
+++ b/psydac/api/tests/test_api_2d_vector.py
@@ -8,7 +8,7 @@
 from sympde.topology import element_of
 from sympde.topology import Square
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -35,8 +35,8 @@ def run_vector_poisson_2d_dir(solution, f, ncells, degree):
     l = LinearForm(v, int_0(expr))
 
     error  = Matrix([u[0]-solution[0], u[1]-solution[1]])
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     bc = EssentialBC(u, 0, domain.boundary)
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
diff --git a/psydac/api/tests/test_api_2d_vector_mapping.py b/psydac/api/tests/test_api_2d_vector_mapping.py
index 34deebe40..69c308cfb 100644
--- a/psydac/api/tests/test_api_2d_vector_mapping.py
+++ b/psydac/api/tests/test_api_2d_vector_mapping.py
@@ -10,7 +10,7 @@
 from sympde.topology import Domain
 from sympde.topology import Union
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -47,8 +47,8 @@ def run_vector_poisson_2d_dir(filename, solution, f):
     l = LinearForm(v, int_0(expr))
 
     error  = Matrix([u[0]-solution[0], u[1]-solution[1]])
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     bc = EssentialBC(u, 0, domain.boundary)
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
diff --git a/psydac/api/tests/test_api_2d_vector_multipatch_mapping.py b/psydac/api/tests/test_api_2d_vector_multipatch_mapping.py
index d35b1bc2e..5188de2a7 100644
--- a/psydac/api/tests/test_api_2d_vector_multipatch_mapping.py
+++ b/psydac/api/tests/test_api_2d_vector_multipatch_mapping.py
@@ -10,7 +10,7 @@
 from sympde.topology import Domain
 from sympde.topology import Union
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from sympde.calculus import minus, plus
@@ -62,8 +62,8 @@ def run_vector_poisson_2d_dir(filename, solution, f):
     l = LinearForm(v, int_0(expr))
 
     error  = Matrix([0, u[1]-solution[1]])
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     bc = EssentialBC(u, 0, domain.boundary)
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
diff --git a/psydac/api/tests/test_api_3d_scalar.py b/psydac/api/tests/test_api_3d_scalar.py
index 4394fa50e..6760b4352 100644
--- a/psydac/api/tests/test_api_3d_scalar.py
+++ b/psydac/api/tests/test_api_3d_scalar.py
@@ -11,7 +11,7 @@
 from sympde.topology import Cube
 from sympde.topology import Union
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -38,8 +38,8 @@ def run_poisson_3d_dir(solution, f, ncells, degree, comm=None):
     l = LinearForm(v, int_0(expr))
 
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     bc = EssentialBC(u, 0, domain.boundary)
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
@@ -113,8 +113,8 @@ def run_poisson_3d_dirneu(solution, f, boundary, ncells, degree, comm=None):
     l = LinearForm(v, expr)
 
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     B_dirichlet = domain.boundary.complement(B_neumann)
     bc = EssentialBC(u, 0, B_dirichlet)
diff --git a/psydac/api/tests/test_api_3d_scalar_mapping.py b/psydac/api/tests/test_api_3d_scalar_mapping.py
index 708ca4e56..2aa9e9219 100644
--- a/psydac/api/tests/test_api_3d_scalar_mapping.py
+++ b/psydac/api/tests/test_api_3d_scalar_mapping.py
@@ -12,7 +12,7 @@
 from sympde.topology import Union
 from sympde.topology import Domain
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -49,8 +49,8 @@ def run_poisson_3d_dir(filename, solution, f, comm=None):
     l = LinearForm(v, int_0(expr))
 
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     bc = EssentialBC(u, 0, domain.boundary)
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
@@ -124,8 +124,8 @@ def run_poisson_3d_dirneu(filename, solution, f, boundary, comm=None):
     l = LinearForm(v, expr)
 
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     B_dirichlet = domain.boundary.complement(B_neumann)
     bc = EssentialBC(u, 0, B_dirichlet)
@@ -196,8 +196,8 @@ def run_laplace_3d_neu(filename, solution, f, comm=None):
     l = LinearForm(v, expr)
 
     error  = u - solution
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v))
     # ...
diff --git a/psydac/api/tests/test_api_3d_vector.py b/psydac/api/tests/test_api_3d_vector.py
index 92470862d..f2171a37d 100644
--- a/psydac/api/tests/test_api_3d_vector.py
+++ b/psydac/api/tests/test_api_3d_vector.py
@@ -8,7 +8,7 @@
 from sympde.topology import element_of
 from sympde.topology import Cube
 from sympde.expr     import BilinearForm, LinearForm, integral
-from sympde.expr     import Norm
+from sympde.expr     import Norm, SemiNorm
 from sympde.expr     import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -35,8 +35,8 @@ def run_vector_poisson_3d_dir(solution, f, ncells, degree):
     l = LinearForm(v, int_0(expr))
 
     error  = Matrix([u[0]-solution[0], u[1]-solution[1], u[2]-solution[2]])
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     bc = EssentialBC(u, 0, domain.boundary)
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
diff --git a/psydac/api/tests/test_api_3d_vector_mapping.py b/psydac/api/tests/test_api_3d_vector_mapping.py
index b3b04a0b3..706070e28 100644
--- a/psydac/api/tests/test_api_3d_vector_mapping.py
+++ b/psydac/api/tests/test_api_3d_vector_mapping.py
@@ -9,7 +9,7 @@
 from sympde.topology import element_of
 from sympde.topology import Domain
 from sympde.expr import BilinearForm, LinearForm, integral
-from sympde.expr import Norm
+from sympde.expr import Norm, SemiNorm
 from sympde.expr import find, EssentialBC
 
 from psydac.api.discretization import discretize
@@ -46,8 +46,8 @@ def run_vector_poisson_3d_dir(filename, solution, f):
     l = LinearForm(v, int_0(expr))
 
     error  = Matrix([u[0]-solution[0], u[1]-solution[1], u[2]-solution[2]])
-    l2norm = Norm(error, domain, kind='l2')
-    h1norm = Norm(error, domain, kind='h1')
+    l2norm =     Norm(error, domain, kind='l2')
+    h1norm = SemiNorm(error, domain, kind='h1')
 
     bc = EssentialBC(u, 0, domain.boundary)
     equation = find(u, forall=v, lhs=a(u,v), rhs=l(v), bc=bc)
diff --git a/psydac/api/tests/test_assembly.py b/psydac/api/tests/test_assembly.py
index 6891b2e66..9a87516a8 100644
--- a/psydac/api/tests/test_assembly.py
+++ b/psydac/api/tests/test_assembly.py
@@ -294,7 +294,7 @@ def test_assemble_complex_parallel(backend):
     ar = BilinearForm((u, v), integral(domain, gr * u * v))
     lc = LinearForm(v, integral(domain, gc * v))
     lr = LinearForm(v, integral(domain, gr * v))
-    nr = Norm(1.0*v, domain, kind='l2')
+    nr = Norm(1.0 *v, domain, kind='l2')
     nc = Norm(1.0j*v, domain, kind='l2')
 
     ncells = (5, 5)
diff --git a/pyproject.toml b/pyproject.toml
index 50b051a68..b68b6f592 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -32,7 +32,7 @@ dependencies = [
     'pyevtk',
 
     # Our packages from PyPi
-    'sympde == 0.18.0',
+    'sympde == 0.18.1',
     'pyccel == 1.8.1',
     'gelato == 0.12',