Add a symmetrized CG stokes example

test/stokes/CMakeLists.txt

@@ -7,6 +7,11 @@ dune_add_formcompiler_system_test(UFLFILE stokes.ufl
                                   INIFILE stokes.mini
                                   )
 
+dune_add_formcompiler_system_test(UFLFILE stokes_sym.ufl
+                                  BASENAME stokes_sym
+                                  INIFILE stokes_sym.mini
+                                  )
+
 dune_add_formcompiler_system_test(UFLFILE stokes_dg.ufl
                                   BASENAME stokes_dg
                                   INIFILE stokes_dg.mini

test/stokes/stokes_sym.mini

+__name = stokes_sym_{__exec_suffix}
+__exec_suffix = symdiff, numdiff | expand num
+
+lowerleft = 0.0 0.0
+upperright = 1.0 1.0
+elements = 16 16
+elementType = simplical
+printmatrix = false
+
+[wrapper.vtkcompare]
+name = {__name}
+reference = hagenpoiseuille_ref
+extension = vtu
+
+[formcompiler]
+numerical_jacobian = 0, 1 | expand num
+exact_solution_expression = g
+compare_l2errorsquared = 1e-6
+print_transformations = True
+print_transformations_dir = .

test/stokes/stokes_sym.ufl

+v_bctype = Expression("if (x[0] < 1. - 1e-8) return 1; else return 0;", on_intersection=True)
+g_v = Expression(("4*x[1]*(1.-x[1])", "0.0"))
+g_p = Expression("8*(1.-x[0])")
+
+g = g_v * g_p
+
+cell = triangle
+P2 = VectorElement("Lagrange", cell, 2, dirichlet_constraints=v_bctype, dirichlet_expression=g_v)
+P1 = FiniteElement("Lagrange", cell, 1)
+TH = P2 * P1
+
+v, q = TestFunctions(TH)
+u, p = TrialFunctions(TH)
+
+ds = ds(subdomain_data=v_bctype, subdomain_id=0)
+n = FacetNormal(triangle)('+')
+
+r = (inner(2*sym(grad(u)), grad(v)) - div(v)*p - q*div(u))*dx - inner(grad(u).T*n,v)*ds
+
+forms = [r]