hp-Finite Element Methods for Singular Perturbations

von Jens M. Melenk

326 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783540442011
• Sprache: Englisch
• Erscheinungsdatum: 10.10.2002
• Genre: Mathematik/Analysis
• Verlag: Springer Berlin