Encyclopedia of Applied and Computational Mathematics

2015 Edition
| Editors: Björn Engquist

Adaptive Mesh Refinement

  • Robert D. Russell
Reference work entry
DOI: https://doi.org/10.1007/978-3-540-70529-1_341

Synonyms

Adaptive grid refinement; Adaptive regridding; Adaptive remeshing

Short Definition

A major challenge when solving a PDE in numerical simulation is the need to improve the quality of a given computational mesh. A desired mesh would typically have a high proportion of its points in the subdomain(s) where the PDE solution varies rapidly, and to avoid oversampling, few points in the rest of the domain. Given a mesh, the goal of an adaptive mesh refinement or remeshing process is to locally refine and coarsen it so as to obtain solution resolution with a minimal number of mesh points, thereby achieving economies in data storage and computational efficiency.

Basic Principles of Adaptive Refinement

A ubiquitous need for mesh adaptivity for a wide array of science and engineering problems has led to the development of a profusion of methods. This has made mesh adaptivity both an extremely active, multifaceted area of research and a common stumbling block for the potential user looking...

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References

  1. 1.
    Alliez, P., Ucelli, G., Gotsman, C., Attene, M.: Recent advances in remeshing of surfaces. In: De Floriani, L., Spagnuolo, M. (eds.) Shape Analysis and Structuring, Mathematics and Visualization, pp. 53–82. Springer, New York (2008)CrossRefGoogle Scholar
  2. 2.
    Bangerth, W., Rannacher, R.: Adaptive Finite Element Methods for Differential Equations. Lectures in Mathematics, p. 207. Birkhauser Verlag, Basel (2003)Google Scholar
  3. 3.
    Huang, W., Russell, R.D.: Adaptive Moving Meshes, p. 432. Springer, New York (2011)Google Scholar
  4. 4.
    Plewa, T., Linde, T., Weirs, V.G. (eds.): Adaptive Mesh Refinement – Theory and Applications. Series in Lecture Notes in Computational Science and Engineering, vol. 41, p. 554. Springer, New York (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Robert D. Russell
    • 1
  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada