Series: Studies in Mathematics and its Applications

Reliable Methods for Computer Simulation

Most recent volume


Volume 33. Reliable Methods for Computer Simulation

Published: 25th July 2004 Editors: Pekka Neittaanmäki Sergey Repin
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.

Additional volumes


Volume 32. Numerical Analysis of Wavelet Methods

Published: 29th April 2003 Editors: A. Cohen

Volume 31. Nonlinear Partial Differential Equations and Their Applications

Published: 21st June 2002 Editors: D. Cioranescu J.-L. Lions†

Volume 30. Operator Theory and Numerical Methods

Published: 3rd July 2001 Editors: H. Fujita N. Saito T. Suzuki

Volume 28. Computer Solution of Large Linear Systems

Published: 16th June 1999 Editors: Gerard Meurant

Volume 27. Mathematical Elasticity

Published: 22nd July 1997 Editors: Author Unknown

Volume 26. Mathematical Problems in Elasticity and Homogenization

Published: 2nd November 1992 Editors: O.A. Oleinik A.S. Shamaev G.A. Yosifian

Volume 25. Attractors of Evolution Equations

Published: 9th March 1992 Editors: A.V. Babin M.I. Vishik

Volume 24. Pseudo-Differential Operators on Manifolds with Singularities

Published: 17th October 1991 Editors: B.-W. Schulze

Volume 23. Singular Perturbations I

Published: 16th August 1990 Editors: L.S. Frank

Volume 22. Boundary Value Problems in Mechanics of Nonhomogeneous Fluids

Published: 18th December 1989 Editors: S.N. Antontsev A.V. Kazhiktov V.N. Monakhov

Volume 21. Scattering Theory for Hyperbolic Operators

Published: 20th November 1989 Editors: V. Petkov

Volume 19. Difference Schemes

Published: 1st May 1987 Editors: S.K. Godunov V.S. Ryabenkii

Volume 17. Mathematical Models and Finite Elements for Reservoir Simulation

Published: 1st January 1986 Editors: G. Chavent J. Jaffré

Volume 16. Mathematical Models in Environmental Problems

Published: 1st January 1986 Editors: G.I. Marchuk

Volume 15. Augmented Lagrangian Methods

Published: 1st July 1983 Editors: M. Fortin R. Glowinski

Volume 14. Introduction to the Theory of Linear Partial Differential Equations

Published: 1st January 1982 Editors: J. Chazarain A. Piriou

Volume 13. Spectral Transform and Solitons

Published: 1st January 1982 Editors: F. Calogero A. Degasperis

Volume 12. Applications of Variational Inequalities in Stochastic Control

Published: 1st January 1982 Editors: A. Bensoussan J.-L. Lions

Volume 11. Stochastic Control by Functional Analysis Methods

Published: 1st January 1982 Editors: A. Bensoussan

Volume 10. Enzyme mathematics

Published: 1st April 2000

Volume 9. Asymptotic Analysis of Singular Perturbations

Published: 1st January 1979 Editors: W. Eckhaus

Volume 8. Numerical Analysis of Variational Inequalities

Published: 1st January 1981 Editors: R. Trémolières J.-L. Lions R. Glowinski

Volume 7. Mathematical Methods of Game and Economic Theory

Published: 1st July 1982 Editors: J.-P. Aubin

Volume 6. Theory of extremal problems

Published: 1st April 2000

Volume 5. Asymptotic Analysis for Periodic Structures

Published: 1st January 1978 Editors: G. Papanicolau A. Bensoussan J.-L. Lions

Volume 4. The Finite Element Method for Elliptic Problems

Published: 1st January 1978 Editors: P.G. Ciarlet

Volume 3. Differential forms in mathematical physics

Published: 1st April 2000

Volume 2. Mathematical Problems in Elasticity and Homogenization

Published: 1st April 2000 Editors: O.A. Oleinik A.S. Shamaev G.A. Yosifian

Patterns and Waves

Published: 1st January 1986 Editors: T. Nishida M. Mimura H. Fujii

Navier-Stokes Equations

Published: 1st July 1984 Editors: R. Temam

Differential Forms in Mathematical Physics

Published: 1st January 1978 Editors: C. Von Westenholz

Volume 1. Convex analysis and variational problems

Published: 1st January 1976