Mathematical Theory of Finite and Boundary Element Methods

Mathematical Theory of Finite and Boundary Element Methods by Albert H. Schatz, Vidar Thomée, Wolfgang L. Wendland.

These are the lecture notes of the seminar "Mathematische Theorie der finiten Element­ und Randelementmethoden" organized by the "Deutsche Mathematiker-Vereinigung" and held in Dusseldorf from 07. - 14. of June 1987. Finite element methods and the closely related boundary element...

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Bibliographic Details
Main Authors: Schatz, Albert H. (Author), Thomée, Vidar (Author), Wendland, Wolfgang L. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 1990.
Series:DMV Seminar ; 15
Springer eBook Collection.
Subjects:
Science.
Electronic resources (E-books)
Online Access:http://dx.doi.org/10.1007/978-3-0348-7630-8
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I: An Analysis of the Finite Element Method for Second Order Elliptic Boundary Value Problems
  • O. Introduction
  • 1. Some function spaces, notation and preliminaries
  • 2. Some finite element spaces and their properties
  • 3. Orthogonal projections onto finite element spaces in L2, in H1 and H01
  • 4. Galerkin finite element method for second order elliptic boundary value problems. Basic Hl and L2 estimates
  • 5. Indefinite second order elliptic problems
  • 6. Local error estimates
  • 7. An introduction to grid refinement. An application to boundary value problems with non-convex corners
  • 8. Maximum norm estimates for the L2 projection. A method using weighted norms
  • 9. Maximum norm estimates for the Galerkin finite element method for second order elliptic problems
  • References
  • II: The Finite Element Method for Parabolic Problems
  • 1. Introduction
  • 2. Non-smooth data error estimates for the semidiscrete problem
  • 3. Completely discrete schemes
  • 4. A nonlinear problem
  • References
  • III: Boundary Element Methods for Elliptic Problems
  • 1 Boundary Integral Equations
  • 2 The Characterization of Boundary Integral Operators and Galerkin Boundary Element Methods
  • 3 Collocation Methods
  • 4 Concluding Remarks.

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