Nitsche’s method for general boundary conditions

Abstract

We introduce a method for treating general boundary conditions in the finite element method generalizing an approach, due to Nitsche (1971), for approximating Dirichlet boundary conditions. We use Poisson's equations as a model problem and prove a priori and a posteriori error estimates. The method is also compared with the traditional Galerkin method. The theoretical results are verified numerically. © 2008 American Mathematical Society.