Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains

Abstract

The hp-version of the finite element method is applied to singularly perturbed reaction-diffusion type equations on polygonal domains. The solution exhibits boundary layers as well as corner layers. On a class of meshes that are suitable refined near the boundary and the corners, robust exponential convergence (in the polynomial degree) is shown in both a balanced norm and the maximum norm.

References in corpus (3)

• Robust exponential convergence of $hp$-FEM in balanced norms for singularly perturbed reaction-diffusion equations
• Multidimensional Butterfly Factorization
• Directional H2-matrix compression for high-frequency problems

Cited by in corpus (5)

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