Averaging technique for FE – a posteriori error control in elasticity. Part I: Conforming FEM

• Published in: Computer methods in applied mechanics and engineering Vol. 190; no. 18; pp. 2483 - 2498
• Main Authors: Carstensen, Carsten, Funken, Stefan A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2001; Elsevier
• Subjects: A posteriori error estimates; Adaptive algorithm; Computational techniques; Elasticity; Exact sciences and technology; Finite element method; Finite-element and galerkin methods; Mathematical methods in physics; Numerical approximation and analysis; Ordinary and partial differential equations, boundary value problems; Physics; Reliability; Finite element method; 65R20; Adaptive algorithm; Elasticity; A posteriori error estimates; Reliability; 73C50; 65N30; Second order equation; Averaging method; Partial differential equations; Error estimation; A posteriori estimation; Numerical method
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(00)00248-6

Averaging techniques are popular tools in adaptive finite element methods for the numerical treatment of second-order partial differential equations since they provide efficient a posteriori error estimates by a simple postprocessing. In this paper, the reliability of any averaging estimator is shown for low order finite element methods in elasticity. Theoretical and numerical evidence supports that the reliability is up to the smoothness of given right-hand sides and independent of the structure of a shape-regular mesh.