Lecture Notes in Mathematics

Melenk, Jens M.

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.

Details

Published by: Springer

Publication Date: 2002-10-10

Format: Paperback

ISBN-13: 9783540442011

DOI: 10.1007/b84212

Dimensions: 235cm x155cm

Pages: 326