HP-finite element methods for singular perturbations

Author(s)

• Melenk, Jens M.

Bibliographic Information

HP-finite element methods for singular perturbations

Jens M. Melenk

（Lecture notes in mathematics, 1796）

Springer, c2002

Note

Bibliography: p. [311]-316

Includes index

Description and Table of Contents

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.

Table of Contents

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.

by "Nielsen BookData"

Details

• NCID: BA59425988
• ISBN:
  • 3540442014
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin ; Tokyo
• Pages/Volumes: xiv, 318 p.
• Size: 24 cm
• Classification:
  • DC21 : 515.353
• Subject Headings:
  • LCSH : Differential equations, Partial -- Numerical solutions
  • LCSH : Singular perturbations (Mathematics)
• Parent Bibliography ID:
  • BA00146586