Error Control and Adaptivity in Scientific Computing

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Haydar Bulgak, Christoph Zenger
Springer Science & Business Media, Jun 30, 1999 - Mathematics - 354 pages
One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc.
Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models.
 

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Contents

Interval Arithmetic Tools for Range Approximation and Inclusion of Zeros
1
A New Concept of Construction of Adaptive Calculation MOdels for Hyperbolic Problems
23
Error Estimates in Linear Systems
65
Error Estimates in Padé Approximation
75
Error Estimates and Convergence Acceleration
87
Pseudoeigenvalues Spectral Portrait of a Matrix and their Connections with Different Criteria of Stability
95
Error Control for Adaptive Sparse Grids
125
Orthogonal Matrix Decompositions in Systems and Control
159
Model Reduction of LargeScale Systems and Control
177
Adaptive Symplectic and Reversible Integrators
191
Domain Decomposition Methods for Compressible Flows
221
Error Control in Finite Element Computations An introduction to error estimation and the meshsize adaption
247
Verified Solution of Large Linear and Nonlinear Systems
279
The Accuracy of Numerical Models for Continuum Problems
299
Domain Decomposition Methods for Elliptic Partial Differential Equations
325
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Page 353 - Periaux, eds., First International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, 1988, pp.