hp-Finite Element Methods for Singular Perturbations. 1st ed. 2002

種類:

電子ブック

責任表示:

by Jens M. Melenk

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002

著者名:

• Melenk, Jens M.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1796

ISBN:

9783540457817 [354045781X]    

注記:

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.

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