Reliable Methods for Computer Simulation

Error Control and Posteriori Estimates


  • Pekka Neittaanmäki, University of Jyväskylä, Finland
  • Sergey Repin, V.A. Steklov Institute of Mathematics, St. Petersburg, Russian Federation

Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker.In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems.The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time.
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Mathematical modellers, civil engineers, computer scientists, mathematical economists and mathematical biologists.


Book information

  • Published: July 2004
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-51376-2

Table of Contents

Contents 1. Introduction.2. Mathematical background.3. A posteriori estimates for iteration methods.4. A posteriori estimates for finite element approximations.5. Foundations of duality theory.6. Two-sided a posteriori estimates for linear elliptic problems.7. A posteriori estimates for nonlinear variational problems.8. A posteriori estimates for variational inequalities.Bibliography.Notation.Index.