hp-Finite Element Methods for Singular Perturbations [electronic resource] / by Jens M. Melenk.
Material type: TextSeries: Lecture Notes in Mathematics ; 1796Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002Description: XIV, 326 p. online resourceContent type:- text
- computer
- online resource
- 9783540457817
- Global analysis (Mathematics)
- Engineering mathematics
- Mechanical engineering
- Numerical analysis
- Global analysis
- Differential equations, partial
- Analysis
- Mathematical and Computational Engineering
- Mechanical Engineering
- Numerical Analysis
- Global Analysis and Analysis on Manifolds
- Partial Differential Equations
- 515 23
- QA299.6-433
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 blb,e -- 5. Regularity Theory in Countably Normed Spaces -- Part III: Regularity in Terms of Asymptotic Expansions -- 6. Exponentially Weighted Countably Normed Spaces -- Appendix -- References -- Index.
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.
There are no comments on this title.