论文标题
固定不可压缩的磁性水力学方程的后验误差分析
An a posteriori error analysis for the equations of stationary incompressible magnetohydrodynamics
论文作者
论文摘要
磁水动力学（MHD）是用于传导受外部磁场的流体的连续水平模型，例如等离子体和液体金属。 MHD系统的有效和强大的解决方案构成了许多挑战，因为它的非线性，非自我接合和高度耦合的性质。在本文中，我们基于确切的惩罚方法为MHD方程的数值解决方案开发了强大而准确的后验误差估计。误差估计还隔离了一定数量的利息（QOI）中的特定误差贡献，以告知离散选择以获得准确的解决方案。这些估计所需的工具涉及双重参数和可计算的残差。
Magnetohydrodynamics (MHD) is a continuum level model for conducting fluids subject to external magnetic fields, e.g. plasmas and liquid metals. The efficient and robust solution of the MHD system poses many challenges due to it's nonlinear, non self-adjoint, and highly coupled nature. In this paper, we develop a robust and accurate a posteriori error estimate for the numerical solution of the MHD equations based on the exact penalty method. The error estimate also isolates particular contributions of 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.
