Chapter

Adaptive finite element methods, by W. Dörfler

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations

Published in print October 2010 | ISBN: 9780199577040
Published online January 2011 | e-ISBN: 9780191595172 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199577040.003.0006

Series: Numerical Mathematics and Scientific Computation

Adaptive finite element methods, by W. Dörfler

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Chapter 6 describes the idea of a posteriori error estimation and adaptive mesh refinement. The main points are the description of the adaptive finite element algorithm, its convergence and a sketch of the optimal complexity of this algorithm with respect to an approximation class of solutions. As in the last chapter the relations between the strong and weak form of the equations are the key for deriving upper and lower a posteriori error estimates. Quantities of interest are estimated.

Keywords: a posteriori error estimation; adaptive mesh refinement; algorithm; convergence; optimal complexity; quantities of interest

Chapter.  8839 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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