A three-field formulation of the Poisson problem with Nitsche approach

TL;DR

This paper presents a modified three-field formulation of the Poisson problem using Nitsche's method, incorporating a biorthogonal system and stabilization for efficient and accurate boundary condition approximation.

Contribution

It introduces a new stabilized three-field formulation with a biorthogonal system for the Poisson problem using Nitsche's approach, ensuring coercivity and optimal convergence.

Findings

Numerical examples verify the algebraic formulation.

The method achieves optimal convergence rates.

Stabilization ensures coercivity on the entire space.

Abstract

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.