hp-Finite Element Methods for Singular Perturbations
Melenk, Jens M.
hp-Finite Element Methods for Singular Perturbations [electronic resource] / by Jens M. Melenk. - XIV, 326 p. online resource. - Lecture Notes in Mathematics, 1796 0075-8434 ; . - Lecture Notes in Mathematics, 1796 .
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.
9783540457817
10.1007/b84212 doi
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.
QA299.6-433
515
hp-Finite Element Methods for Singular Perturbations [electronic resource] / by Jens M. Melenk. - XIV, 326 p. online resource. - Lecture Notes in Mathematics, 1796 0075-8434 ; . - Lecture Notes in Mathematics, 1796 .
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.
9783540457817
10.1007/b84212 doi
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.
QA299.6-433
515