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Morin, Pedro; Siebert, Kunibert G.; Veeser, Andreas

A basic convergence result for conforming adaptive finite elements. (English) Zbl 1153.65111

Math. Models Methods Appl. Sci. 18, No. 5, 707-737 (2008).
The approximate solution with adaptive finite elements for a class of linear boundary value problems (including saddle point problems) is considered. Refinement relies on unique quasi-regular element subdivisions and generates locally quasi-uniform grids. The finite element spaces are conforming, nested, and satisfy the inf-sup condition. The error estimator is reliable as well as locally and discretely efficient. The marked elements are subdivided at least once. A sufficient and essentially necessary condition for the convergence of the finite element solution to the exact solution is given. This condition is not only satisfied by W. Dörfler’s strategy [SIAM J. Numer. Anal. 33, No.3, 1106–1124 (1996; Zbl 0854.65090)], but also by the maximum strategy and the equidistribution strategy.
Reviewer: Wilhelm Heinrichs (Essen)

Cited in 68 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

Keywords:

Adaptivity; conforming finite elements; convergence

Citations:

Zbl 0854.65090

Software:

ALBERTA
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\textit{P. Morin} et al., Math. Models Methods Appl. Sci. 18, No. 5, 707--737 (2008; Zbl 1153.65111)
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