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- catalog abstract "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.".
- catalog contributor b12644005.
- catalog created "c2002.".
- catalog date "2002".
- catalog date "c2002.".
- catalog dateCopyrighted "c2002.".
- catalog description "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.".
- catalog description "Includes bibliographical references (p. [311]-316) and index".
- catalog description "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.".
- catalog extent "xiv, 318 p. :".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540442014 (softcover : alk. paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1796.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1796".
- catalog issued "2002".
- catalog issued "c2002.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "515/.353 21".
- catalog subject "Differential equations, Partial Numerical solutions.".
- catalog subject "Differential equations, partial.".
- catalog subject "Global analysis (Mathematics)".
- catalog subject "Mathematics.".
- catalog subject "Numerical analysis.".
- catalog subject "QA377 .M325 2002".
- catalog subject "Singular perturbations (Mathematics)".
- catalog tableOfContents "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.".
- catalog title "hp-finite element methods for singular perturbations / Jens M. Melenk.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".