hp-Finite Element Methods for Singular Perturbations

• Main Author: Melenk, Jens M. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1796
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Applied mathematics.; Engineering mathematics.; Mechanical engineering.; Numerical analysis.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Analysis.; Mathematical and Computational Engineering.; Mechanical Engineering.; Numerical Analysis.; Global Analysis and Analysis on Manifolds.; Partial Differential Equations.

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-co...

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.