Averaging techniques for reliable and efficient a posteriori finite element error control : analysis and applications.

摘要

Local averaging techniques, which are used to postprocess discrete flux or stress approximations of low-orderudfinite element schemes for elliptic boundary value problems, are applied for error control and adaptive meshudrefinement. We put particular emphasis on the explicit calculation of all constants, arising in the proofs ofudreliability and efficiency, in terms of the known data and quantify the equivalence of local averagingudtechniques. We highlight and discuss a wide selection of applications for which averaging-based estimatorsudprovide highly accurate error control.