Hp-finite element methods for singular perturbations /
Melenk, Jens M., 1967-
Hp-finite element methods for singular perturbations / Jens M. Melenk. - Berlin ; New York : Springer, ©2002. - 1 online resource (xiv, 318 pages) : illustrations - Lecture notes in mathematics, 1796 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1796. .
Includes bibliographical references (pages 311-316) and index.
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.
English.
9783540457817 354045781X
10.1007/b84212 doi (WaSeSS)ssj0000323844
Differential equations, Partial--Numerical solutions.
Singular perturbations (Mathematics)
Équations aux dérivées partielles--Solutions numériques.
Perturbations singulières (Mathématiques)
Perturbaciones singulares (Matemáticas)
Differential equations, Partial--Numerical solutions
Singular perturbations (Mathematics)
Finite-Elemente-Methode
Elliptische Differentialgleichung
Randwertproblem
Singuläre Störung
Équations aux dérivées partielles--Solutions numériques.
Perturbations singulières.
QA3 QA377 / .L28 no. 1796
515/.353
V1043227
Hp-finite element methods for singular perturbations / Jens M. Melenk. - Berlin ; New York : Springer, ©2002. - 1 online resource (xiv, 318 pages) : illustrations - Lecture notes in mathematics, 1796 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1796. .
Includes bibliographical references (pages 311-316) and index.
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.
English.
9783540457817 354045781X
10.1007/b84212 doi (WaSeSS)ssj0000323844
Differential equations, Partial--Numerical solutions.
Singular perturbations (Mathematics)
Équations aux dérivées partielles--Solutions numériques.
Perturbations singulières (Mathématiques)
Perturbaciones singulares (Matemáticas)
Differential equations, Partial--Numerical solutions
Singular perturbations (Mathematics)
Finite-Elemente-Methode
Elliptische Differentialgleichung
Randwertproblem
Singuläre Störung
Équations aux dérivées partielles--Solutions numériques.
Perturbations singulières.
QA3 QA377 / .L28 no. 1796
515/.353
V1043227