Overview
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.
- | Author: Jens M. Melenk
- | Publisher: Springer
- | Publication Date: Oct 10, 2002
- | Number of Pages: 326 pages
- | Binding: Paperback or Softback
- | ISBN-10: 3540442014
- | ISBN-13: 9783540442011
