Title: hp-Finite Element Methods for Singular Perturbations (Lecture Notes in Mathematics)
Publisher: Springer 2009-02-22
Publication Date: 2009
Language: English
ISBN 10: 3540442014
ISBN 13: 9783540442011
Binding: Paperback
Condition: New

About this title

Synopsis

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.

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