A review of unified a posteriori finite element error control

By Carsten Carstensen, Martin Eigel, Ronald H. W. Hoppe, C. Löbhard. 2012

71 citations recorded by the source corpus.

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 corre- sponding residuals is proposed which then allows for the unified estimation of the re- spective 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-Lame, and the semi-discrete eddy current equations.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6825d49f3f4842dddad98625be3fb1099c8e4508

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Adaptive stochastic Galerkin FEM (2014, background): “We refer to [7] for a survey and further references.”