An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems
An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems
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DOI：
10.1137/100782760
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发表时间：
2012-05
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通讯作者：
Sajid Memon;N. Nataraj;A. K. Pani
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作者：
Sajid Memon;N. Nataraj;A. K. Pani
本文给出了二阶线性抛物型初边值问题混合有限元Galerkin逼近的后验误差估计。利用混合椭圆重构，证明了半离散格式解及其通量在$L^{\infty}（L^2）$-和$L^2（L^2）$-模下的后验误差估计.最后，基于向后Euler方法，分析了一个完全离散的格式，并得到了后验误差界，改进了抛物问题混合有限元逼近的后验估计.数值实验的结果验证了估计的效率也被提供。
In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in $L^{\infty}(L^2)$- and $L^2(L^2)$-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided.