Error Analysis of the Stabilized Boundary Penalty Method

Abstract

The Stabilized Boundary Penalty Method (SBMPM) enforces Dirichlet boundary conditions though a penalty function related to the mesh-size. We derive a priori error estimates for this method, and we prove that they always give, at least theoretically, an optimal rate of convergence. We also derive
an a posteriori error estimate and we propose an adaptive loop. Numerical examples show that SBPM is highly flexible, produces accurate results and it is a very efficient adaptive method.