# Redesign of essential boundary conditions

Registered by Marie Rognes

This blueprint has been superseded. See the newer blueprint "Restricted function spaces" for updated plans.

Replace current Dirichlet boundary condition design with constrained function spaces

## Blueprint information

Status:
Complete
Approver:
None
Priority:
Medium
Drafter:
None
Direction:
Needs approval
Assignee:
None
Definition:
Superseded
Series goal:
None
Implementation:
Unknown
Milestone target:
None
Completed by
Anders Logg

### Whiteboard

Problem:

Mathematically, an essential boundary condition is typically associated with a constrained function space. For example: the natural space for the Laplacian with zero Dirichlet boundary conditions is H^1_0.

In DOLFIN on the other hand, an essential boundary condition is represented using a DirichletBC, which acts on the linear algebra level.

Bottomline, there is a certain mismatch between the mathematical abstraction and the current implementation. Further, it tends to be a bit cumbersome to pass the boundary conditions around 'everywhere'.

Suggested fix:

Add the possibility of constraining function spaces:

V = FunctionSpace(...)

domain = SubDomain (or MeshFunction)
g = Expression (or Function)

V.constrain(domain, g)

Implementational thoughts:

- The information about the essential boundary condition should thus now lie with the function space. Hence, no need to send boundary conditions around :)

- I guess the constraint information will only be invoked when assembling element tensors over the function space.

AL: I think this looks good. We could also allow bc as an argument to constrain:

V.constrain(bc)

And we could also allow bc as an argument to the constructor:

V = FunctionSpace(mesh, "CG", 1, bc)

AL: Update. This last suggestion won't work since bc requires V in its constructor. But it makes sense to allow spaces to be constrained. This can work by having V.constrain(domain, g) and letting that call create a DirichletBC stored as part of the FunctionSpace.

(?)

### Work Items

This blueprint contains Public information
Everyone can see this information.