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9 - Solution adaptation

from Part III - Solution verification

Published online by Cambridge University Press:  05 March 2013

William L. Oberkampf  and
Christopher J. Roy
Christopher J. Roy
Affiliation:
Virginia Polytechnic Institute and State University
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Summary

The previous chapter focused on the estimation of numerical errors and uncertainties due to the discretization. In addition to estimating the discretization error, we also desire methods for reducing it when either it is found to be too large or when the solutions are not yet in the asymptotic range and therefore the error estimates are not reliable. Applying systematic mesh refinement, although required for assessing the reliability of all discretization error estimation approaches, is not the most efficient method for reducing the discretization error. Since systematic refinement, by definition, refines by the same factor over the entire domain, it generally results in meshes with highly-refined cells or elements in regions where they are not needed. Recall that for 3-D scientific computing applications, each time the mesh is refined using grid halving (a refinement factor of two), the number of cells/elements increases by a factor of eight. Thus systematic refinement for reducing discretization error can be prohibitively expensive.

Targeted, local solution adaptation is a much better strategy for reducing the discretization error. After a discussion of factors affecting the discretization error, this chapter then addresses the two main aspects of solution adaptation:

  1. methods for determining which regions should be adapted and

  2. methods for accomplishing the adaption.

Type
Chapter
Information
Verification and Validation in Scientific Computing , pp. 343 - 368
Publisher: Cambridge University Press
Print publication year: 2010

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