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arXiv · 1312.6460

Residual-based a posteriori error estimation for multipoint flux mixed finite element methods

Shaohong Du·Shuyu Sun·Xiaoping Xie
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Abstract

A novel residual-type {\it a posteriori} error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived {\it a posteriori} error estimator for the velocity and pressure error in $L^{2}-$norm consists of discretization and quadrature indicators, and is shown to be reliable and efficient. The main tools of analysis are a locally postprocessed approximation to the pressure solution of an auxiliary problem and a quadrature error estimate. Numerical experiments are presented to illustrate the competitive behavior of the estimator.

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Shaohong Du, Shuyu Sun, Xiaoping Xie. 2013-12-23. Residual-based a posteriori error estimation for multipoint flux mixed finite element methods. https://arxiv.org/abs/1312.6460

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