The influence and selection of subspaces for a posteriori error estimators
An important ingredient in an adaptive numerical algorithm is a reliable method for assessing the accuracy of the computed approximation. In general, an error estimator or indicator will be based on the obtained solution. Two important requirements have to be satisfied: (a) the cost of the estimator should be small compared to the cost of the computed solution; (b) the estimator should yield realistic error measured in an appropriate fashion. In this paper the author studies the influence of the choice of the subspace used in the element residual problem and proves theoretically the consistency of the estimator. The obtained results provide some practical guidelines for the selection of a posteriori error estimators and establish the limits of their performance. The recommended choice of subspaces may be viewed as being sufficient to filter out spurious modes while retaining a sufficient degree of approximation for the true modes.
scientific article; zbMATH DE number 932022