Convergence and quasi‐optimality of adaptive FEM with inhomogeneous Dirichlet data

Abstract

AbstractWe consider an adaptive mesh‐refining algorithm for a lowest‐order finite element method (AFEM). Contrary to prior works, where the Poisson equation with homogeneous Dirichlet data is analyzed, our focus is on the case of inhomogeneous Dirichlet data g ≠ 0. As is usually done in practice, we use nodal interpolation to discretize g. Besides convergence of AFEM, which is proven by means of an appropriate contraction quantity, we also discuss quasi‐optimality of the proposed algorithm. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)