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A Review of Unified A Posteriori Finite Element Error Control
Published online by Cambridge University Press: 28 May 2015
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.
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- Type
- Research Article
- Information
- Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 4 , November 2012 , pp. 509 - 558
- Copyright
- Copyright © Global Science Press Limited 2012