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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A New Concept of Construction of Adaptive Calculation MOdels for Hyperbolic Problems
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Error Estimates in Padé Approximation
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Adaptive Symplectic and Reversible Integrators
Domain Decomposition Methods for Compressible Flows
Error Control in Finite Element Computations An introduction to error estimation and the meshsize adaption
Verified Solution of Large Linear and Nonlinear Systems
The Accuracy of Numerical Models for Continuum Problems
Domain Decomposition Methods for Elliptic Partial Differential Equations

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Page 353 - Periaux, eds., First International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, 1988, pp.