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Mathematical Theory of Finite and Boundary Element Methods

  • Albert H. Schatz
  • Vidar Thomée
  • Wolfgang L. Wendland

Part of the DMV Seminar book series (OWS, volume 15)

Table of contents

  1. Front Matter
    Pages 1-8
  2. An Analysis of the Finite Element Method for Second Order Elliptic Boundary Value Problems

  3. The Finite Element Method for Parabolic Problems

  4. Boundary Element Methods for Elliptic Problems

    1. Front Matter
      Pages 219-221
    2. Albert H. Schatz, Vidar Thomée, Wolfgang L. Wendland
      Pages 223-238
    3. Albert H. Schatz, Vidar Thomée, Wolfgang L. Wendland
      Pages 239-255
    4. Albert H. Schatz, Vidar Thomée, Wolfgang L. Wendland
      Pages 257-266
    5. Albert H. Schatz, Vidar Thomée, Wolfgang L. Wendland
      Pages 267-268
  5. Back Matter
    Pages 269-276

About this book

Introduction

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 methods nowadays belong to the standard routines for the computation of solutions to boundary and initial boundary value problems of partial differential equations with many applications as e.g. in elasticity and thermoelasticity, fluid mechanics, acoustics, electromagnetics, scatter­ ing and diffusion. These methods also stimulated the development of corresponding mathematical numerical analysis. I was very happy that A. Schatz and V. Thomee generously joined the adventure of the seminar and not only gave stimulating lectures but also spent so much time for personal discussion with all the participants. The seminar as well as these notes consist of three parts: 1. An Analysis of the Finite Element Method for Second Order Elliptic Boundary Value Problems by A. H. Schatz. II. On Finite Elements for Parabolic Problems by V. Thomee. III. I30undary Element Methods for Elliptic Problems by \V. L. Wendland. The prerequisites for reading this book are basic knowledge in partial differential equations (including pseudo-differential operators) and in numerical analysis. It was not our intention to present a comprehensive account of the research in this field, but rather to give an introduction and overview to the three different topics which shed some light on recent research.

Keywords

Boundary value problem Mathematik calculus elasticity mathematics partial differential equation

Authors and affiliations

  • Albert H. Schatz
    • 1
  • Vidar Thomée
    • 2
  • Wolfgang L. Wendland
    • 3
  1. 1.Dept. of MathematicsCornell UniversityIthacaUSA
  2. 2.Dept. of MathematicsChalmers University of Technology University of GöteborgGöteborgSweden
  3. 3.Mathematisches Institut AUniversity of StuttgartStuttgart 80Federal Republic of Germany

Bibliographic information