Dear All,

I’m trying to solve the stokes equation with Pure Neumann boundary conditions or Traction boundary conditions at the boundaries.

This problem is singular and similiar to (https://fenicsproject.org/olddocs/dolfin/1.3.0/python/demo/documented/singular-poisson/python/documentation.html#) because the velocity field and the pressure field are not determined up to a constant .

mesh=UnitSquareMesh(20,20)

V = VectorFunctionSpace(mesh,‘P’, 1)

p_element=FiniteElement(‘P’, mesh.ufl_cell(),1)

v_element=VectorElement(‘P’,mesh.ufl_cell(),2)

element = MixedElement([p_element, v_element])

FS=FunctionSpace(mesh,element)q,v=TestFunctions(FS)

P,u=TrialFunctions(FS)force=df.Expression((‘x[0]’,‘0’),degree=1)

a = inner(grad(u), grad(v))df.dx + div(v)div(u)*df.dxpdf.dx + q

L=inner(force,v)*df.dx

- Can someone help me with how to remove the null space of the Matrix (a), such that i can eliminate constant velocity and pressure solutions ? similiar to (https://fenicsproject.org/qa/4121/help-parallelising-space-method-eliminating-rigid-motion/) .
- For the elasticity problem however there is only one function space. How can one do this procedure for both the pressure and the velocity?