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


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

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