Data oscillation and convergence of adaptive FEM. (English) Zbl 0970.65113

Morin, Pedro; Nochetto, Ricardo H.; Siebert, Kunibert G.

SIAM J. Numer. Anal. 38, No. 2, 466-488 (2000).

The error of a finite element approximation may be split into two terms. One source is the approximation of the right hand side \(f\) by some \(f_H\), and the other one is the error in the solution with \(f_H\). The two contributions are found in a posteriori error estimators. Since the first contribution can be bounded a priori, in most cases more attention is given to the second one which is also dominating in most cases. This paper concentrates on the first term, and an argument on finite dimensional spaces shows that this is necessary if geometric convergence has to be guaranted. Refinement strategies with this aim are investigated.

Reviewer: Dietrich Braess (Bochum)

MSC:

65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65Y20	Complexity and performance of numerical algorithms

Keywords:

data oscillation; a posteriori error estimators; adaptive mesh refinement; finite element; convergence

Software:

ALBERT