2. hp-FEM for Reaction Diffusion Problems: Principal Results

Abstract

• 2.1 Setting and Introduction

• 2.2 Prelude: the one-dimensional case

  • 2.2.1 Regularity in one dimension

  • 2.2.2 hp-FEM in one dimension

  • 2.2.3 Numerical examples

• 2.3 Regularity: the two-dimensional case

• 2.4 hp-FEM approximation

  • 2.4.1 hp-meshes and spaces

  • 2.4.2 The minimal hp-mesh

  • 2.4.3 hp-FEM

• 2.5 Numerical Examples

  • 2.5.1 The classical L-shaped domain

  • 2.5.2 Robustness with respect to mesh distortion

  • 2.5.3 Examples with singular right-hand side

• 2.6 h-FEM approximation

  • 2.6.1 Approximation on Shishkin meshes in one dimension

  • 2.6.2 h-FEM meshes

  • 2.6.3 h-FEM boundary layer meshes