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首页> 外文会议>Proceedings of International Conference on Recent Advances in Adaptive Computation >A Synthesis of A Posteriori Error Estimation Techniques for Conforming, Non-Conforming and Discontinuous Galerkin Finite Element Methods
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A Synthesis of A Posteriori Error Estimation Techniques for Conforming, Non-Conforming and Discontinuous Galerkin Finite Element Methods

机译：一致性，非一致性和间断Galerkin有限元方法的后验误差估计技术的综合

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摘要

A posteriori error estimation for conforming, non-conforming and discontinuous finite element schemes are discussed within a single framework. By dealing with three ostensibly different schemes under the same umbrella, the same common underlying principles at work in each case are highlighted leading to a clearer understanding of the issues involved. The ideas are presented in the context of piecewise affine finite element approximation of a second-order elliptic problem. It is found that the framework leads to three different known a posteriori error estimators: the equilibrated residual method in the case of conforming Galerkin FEM; the estimator of Ainsworth [3] in the case of the Crouzeix-Raviart scheme, and a new estimator [1] recently derived in case of discontinuous Galerkin approximation. In all cases one has computable upper bounds on the error measured in the energy norm and corresponding local lower bounds showing the efficiency of the schemes.
机译：在单个框架内讨论了用于合格，不合格和不连续有限元方案的后验误差估计。通过在同一保护伞下处理三种表面上不同的方案，可以突出显示每种情况下工作中相同的共同基本原理，从而使人们对所涉及的问题有更清晰的了解。这些想法是在二阶椭圆问题的分段仿射有限元逼近的背景下提出的。发现该框架导致了三种不同的已知后验误差估计器：在符合Galerkin FEM的情况下采用了平衡残差法;在Crouzeix-Raviart方案的情况下，是Ainsworth [3]的估计，在不连续Galerkin近似的情况下，最近又得到了新的估计[1]。在所有情况下，对于在能量范数中测得的误差，都有一个可计算的上限，而相应的局部下限则表明了该方案的效率。

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