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Galerkin Finite Element Methods for Parabolic Problems

  • Vidar Thomée

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 25)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Vidar Thomée
    Pages 1-24
  3. Vidar Thomée
    Pages 37-54
  4. Vidar Thomée
    Pages 55-66
  5. Vidar Thomée
    Pages 163-184
  6. Vidar Thomée
    Pages 231-244
  7. Vidar Thomée
    Pages 245-260
  8. Vidar Thomée
    Pages 261-278
  9. Vidar Thomée
    Pages 279-292
  10. Vidar Thomée
    Pages 293-304
  11. Vidar Thomée
    Pages 305-315
  12. Vidar Thomée
    Pages 317-334
  13. Back Matter
    Pages 355-370

About this book

Introduction

This book provides insight in the mathematics of Galerkin finite element method as applied to parabolic equations. The approach is based on first discretizing in the spatial variables by Galerkin's method, using piecewise polynomial trial functions, and then applying some single step or multistep time stepping method. The concern is stability and error analysis of approximate solutions in various norms, and under various regularity assumptions on the exact solution. The book gives an excellent insight in the present ideas and methods of analysis. The second edition has been influenced by recent progress in application of semigroup theory to stability and error analysis, particulatly in maximum-norm. Two new chapters have also been added, dealing with problems in polygonal, particularly noncovex, spatial domains, and with time discretization based on using Laplace transformation and quadrature.

Keywords

Approximation Galerkin methods differential equations finite element method finite element theory maximum parabolic partial

Authors and affiliations

  • Vidar Thomée
    • 1
  1. 1.Department of MathematicsChalmers University of TechnologyGöteborgSweden

Bibliographic information