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A Review of Unified a Posteriori Finite Element Error Control

A Review of Unified a Posteriori Finite Element Error Control
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Year:    2012

Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 4 : pp. 509–558

Abstract

This paper aims at a general guideline to obtain a posteriori error estimates for the finite element error control in computational partial differential equations. In the abstract setting of mixed formulations, a generalised formulation of the corresponding residuals is proposed which then allows for the unified estimation of the respective dual norms. Notably, this can be done with an approach which is applicable in the same way to conforming, nonconforming and mixed discretisations. Subsequently, the unified approach is applied to various model problems. In particular, we consider the Laplace, Stokes, Navier-Lamé, and the semi-discrete eddy current equations.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2011.m1032

Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 4 : pp. 509–558

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    50

Keywords:    A posteriori error analysis finite element method nonconforming finite element method mixed finite element method adaptive algorithm Poisson equation Lamé equations Stokes equations Maxwell equations unified a posteriori error analysis discontinuous Galerkin residual estimator.

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