A note on p/hp finite element methods for reaction-diffusion problems in polygonal domains

Abstract

We present guidelines on how to choose the mesh and polynomial degree distribution for the approximation of reaction-diffusion problems in polygonal domains, in the context of the hp finite element method. These guidelines take into account the presence of both boundary layers and corner singularities in the solution. We present the results of numerical computations showing that robust, (near) exponential rates of convergence can be achieved using this technique. Copyright (C) 2000 John Wiley and Sons, Ltd. We present guidelines on how to choose the mesh and polynomial degree distribution for the approximation of reaction-diffusion problems in polygonal domains, in the context of the hp finite element method. These guidelines take into account the presence of both boundary layers and corner singularities in the solution. We present the results of numerical computations showing that robust, (near) exponential rates of convergence can be achieved using this technique.