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首页> 外文期刊>Journal of Computational Physics >A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates
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A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

机译：基于分层后验误差估计的各向异性网格自适应新方法

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摘要

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gau?-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.
机译：提出了一种新的各向异性网格自适应椭圆微分方程有限元求解策略。它在某些度量空间中生成各向异性自适应网格，作为准均匀网格，其中度量张量是基于分层后验误差估计来计算的。本研究采用全局分层误差估计以获得解决方案的可靠方向信息。我们没有完全解决通常要付出高昂代价的全局错误问题，而是使用对称Gau？-Seidel方法迭代地解决了该问题。数值结果表明，几次GS迭代足以获得用于各向异性网格自适应的误差的合理良好近似值。将该新方法与使用局部误差估计器或恢复的Hessians的几种策略进行比较。给出了数值结果，供选择的测试示例和数学模型用于材料系数中正交异性大的热电池的热传导。

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