SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page B354-B380, January 2021.
Resistive magnetohydrodynamics (MHD) is a continuum base-level model for conducting fluids (e.g., plasmas and liquid metals) subject to external magnetic fields. The efficient and robust solution of the MHD system poses many challenges due to the strongly nonlinear, non--self-adjoint, and highly coupled nature of the physics. In this article, we develop a robust and accurate a posteriori error estimate for the numerical solution of the resistive MHD equations based on the exact penalty method. The error estimate also isolates particular contributions to the error in a quantity of interest (QoI) to inform discretization choices to arrive at accurate solutions. The tools required for these estimates involve duality arguments and computable residuals.

中文翻译：

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平稳不可压缩磁流体动力学方程的后验误差分析

SIAM科学计算杂志，第43卷，第2期，第B354-B380页，2021年1月。
电阻磁流体动力学（MHD）是连续的基本模型，用于传导受外部磁场作用的流体（例如，等离子体和液态金属）。由于物理的强非线性，非自伴和高度耦合性质，MHD系统的有效而强大的解决方案提出了许多挑战。在本文中，我们基于精确罚分法为电阻MHD方程的数值解开发了鲁棒且准确的后验误差估计。误差估计还可以将感兴趣量（QoI）的特定误差隔离开来，以告知离散化选择以得出准确的解决方案。这些估计所需的工具涉及对偶论证和可计算的残差。