Averaging Techniques for Reliable and Efficient A Posteriori Finite Element Error Control: Analysis and Applications

Carstensen, Carsten; Jensen, Max

Abstract

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

Citation

Carstensen, C., & Jensen, M. (2005). Averaging Techniques for Reliable and Efficient A Posteriori Finite Element Error Control: Analysis and Applications. In Z. Shi, Z. Chen, T. Tang, & D. Yu (Eds.), Recent advances in adaptive computation (15-34). American Mathematical Society

• Publication Date: Dec 1, 2005
• Deposit Date: Jul 24, 2007
• Publicly Available Date: Jul 24, 2007
• Publisher: American Mathematical Society
• Pages: 15-34
• Series Title: Contemporary mathematics
• Book Title: Recent advances in adaptive computation.
• Public URL: https://durham-repository.worktribe.com/output/1666316
• Publisher URL: http://www.oup.com/uk/catalogue/?ci=9780821836620
• Additional Information: Series: Contemporary Mathematics ; 383.