A Posteriori Error Estimators and Adaptivity for Finite Element Approximation of the Non-Homogeneous Dirichlet Problem

Techniques are developed for a posteriori error analysis of the non-homogeneous Dirichlet problem for the Laplacian giving computable error bounds for the error measured in the energy norm. The techniques are based on the equilibrated residual method that has proved to be reliable and accurate for the treatment of problems with homogeneous Dirichlet data. It is shown how the equilibrated residual method must be modified to include the practically important case of non-homogeneous Dirichlet data. Explicit and implicit a posteriori error estimators are derived and shown to be efficient and reliable. Numerical examples are provided illustrating the theory.