Hp-finite element methods for singular perturbations
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 …
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- Full title :Hp-finite element methods for singular perturbations / Jens M. Melenk.
Summary
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.
Read More ↓Edition Statements
- Publication Date:©2002.
Publication Statements
- Publisher(s):Springer
- Place of Publication:Berlin
- Language:eng
- Publication Date:©2002.
The Physical Object
- Description:xiv, 318 pages : : illustrations ; : 24 cm
Edition Identifiers
- ISBN:3540442014, 9783540442011
- oclc:ocm50478472
- LC Classification:QA377
- Dewey Decimal:515/.353
Table of Contents
1. Introduction --- Part I. Finite Element Approximation. 2. hp-FEM for Reaction Diffusion Problems: Principal Results --- 3. hp Approximation --- Part II. Regularity in Countably Normed Spaces --- 4. The Countably Normed Spaces Bl --- 5. Regularity Theory in Countably Normed Spaces --- Part III. Regularity in Terms of Asymptotic Expansions. 6. Exponentially Weighted Countably Normed Spaces --- 7. Regularity through Asymptotic Expansions --- Appendixes.
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