Adaptive Finite Element Methods: A Review

[+] Author and Article Information
Long-yuan Li

Department of Civil Engineering, Aston University, Aston Triangle, Birmingham B4 7ET, UK

Peter Bettess

School of Engineering, Science Laboratories, University of Durham, Durham DH1 3LE, UK

Appl. Mech. Rev 50(10), 581-591 (Oct 01, 1997) (11 pages) doi:10.1115/1.3101670 History: Online April 20, 2009


The adaptive finite element method (FEM) was developed in the early 1980s. The basic concept of adaptivity developed in the FEM is that, when a physical problem is analyzed using finite elements, there exist some discretization errors caused owing to the use of the finite element model. These errors are calculated in order to assess the accuracy of the solution obtained. If the errors are large, then the finite element model is refined through reducing the size of elements or increasing the order of interpolation functions. The new model is re-analyzed and the errors in the new model are recalculated. This procedure is continued until the calculated errors fall below the specified permissible values. The key features in the adaptive FEM are the estimation of discretization errors and the refinement of finite element models. This paper presents a brief review of the methods for error estimates and adaptive refinement processes applied to finite element calculations. The basic theories and principles of estimating finite element discretization errors and refining finite element models are presented. This review article contains 131 references.

Copyright © 1997 by American Society of Mechanical Engineers
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