A three-field formulation of the Poisson problem with Nitsche approach
Incremental improvement for numerical methods solving Poisson problems with Dirichlet boundary conditions.
The paper modifies a three-field formulation of the Poisson problem using Nitsche's method to weakly impose Dirichlet boundary conditions while preserving optimal convergence. Numerical examples verify the algebraic formulation.
We modify a three-field formulation of the Poisson problem with Nitsche approach for approximating Dirichlet boundary conditions. Nitsche approach allows us to weakly impose Dirichlet boundary condition but still preserves the optimal convergence. We use the biorthogonal system for efficient numerical computation and introduce a stabilisation term so that the problem is coercive on the whole space. Numerical examples are presented to verify the algebraic formulation of the problem.