Jørgen S. Dokken (Simula Research Laboratory)

To solve partial differential equations, it is essential to specify the behavior of the solution at the edges of the domain. Without boundary conditions, it is not possible to uniquely determine a solution. Common boundary conditions include the Dirichlet, Neumann and Robin-type conditions. These can be enforced weakly through the variational formulation. Dirichlet conditions can also be applied by using lifting, strongly enforcing the boundary condition on the discrete level. The Unified Form Language (UFL) makes it easy to represent these types of boundary conditions in FEniCS.

However, there are many boundary conditions that cannot be trivially expressed with UFL, including periodic boundary conditions, contact conditions and strong enforcement of slip conditions. In this talk, I will present various ways of extending the FEniCS software to handle such conditions, using multi-point constraints and an unbiased Nitsche’s formulation to enforce contact constraints.