FEM-analysis on Layer-adapted Meshes for Turning Point Problems Exhibiting an Interior Layer

Abstract

We consider singularly perturbed turning point problems whose solutions exhibit an interior layer. Two suitable layer-adapted mesh-types are presented. For both types we give uniform error estimates in the ε-weighted energy norm for finite elements of higher order. Numerical experiments are used to compare the meshes and to confirm the theoretical findings.

Keywords

• singular perturbation
• turning point
• interior layer
• layer-adapted meshes
• higher order finite elements