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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
113/2005

Function, Gradient and Hessian Recovery Using Quadratic Edge-Bump Functions

Jeffrey Ovall

Abstract

An approximate error function for the discretization error on a given mesh is obtained by projecting (via the energy inner product) the functional residual onto the space of continuous, piecewise quadratic functions which vanish on the vertices of the mesh. Conditions are given under which one can expect this hierarchical basis error estimator to give efficient and reliable function recovery, asymptotically exact gradient recovery and convergent Hessian recovery in the square norms. One does not find similar function recovery results in the literature. The analysis given here is based on a certain superconvergence result which has been used elsewhere in the analysis of gradient recovery methods. Numerical experiments are provided which demonstrate the effectivity of the approximate error function in practice.

Received:
Nov 30, 2005
Published:
Nov 30, 2005
MSC Codes:
65N15, 65N30, 65N50
Keywords:
finite elements, error estimation, hierarchical bases

Related publications

inJournal
2007 Repository Open Access
Jeffrey S. Ovall

Function, gradient, and Hessian recovery using quadratic edge-bump functions

In: SIAM journal on numerical analysis, 45 (2007) 3, pp. 1064-1080