一种用于二维非光滑和非凸域磁流体动力学方程的收敛线性化拉格朗日有限元方法
A convergent linearized Lagrange finite element method for the magneto-hydrodynamic equations in 2D nonsmooth and nonconvex domains
AI总结：
本文提出了一种全新的完全离散线性化H¹连续拉格朗日有限元方法，用于求解基于磁势形式的二维磁流体动力学方程。该方法在一般域中能够收敛，包括非凸、非光滑和多连通的区域。仅基于初始条件和源项的正则性证明了数值解的子序列收敛性，无需额外假设解的正则性。对于u和H的数值解，证明了在L²(0,T;L²(Ω))中的强收敛性，无需任何网格限制。
摘要：
本文提出了一种全新的完全离散线性化H¹-连续拉格朗日有限元方法，用于求解基于磁势形式的二维磁流体动力学方程。所提出的方法在一般域中能够收敛，这些域可能是非凸、非光滑和多连通的。仅基于初始条件和源项的正则性，证明了数值解的子序列收敛性，而无需对解的正则性做额外假设。对于u和H的数值解，证明了在L²(0,T;L²(Ω))中的强收敛性，无需任何网格限制。
英文摘要：
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical solutions that converge in general domains that may be nonconvex, nonsmooth and multi-connected. The convergence of subsequences of the numerical solutions is proved only based on the regularity of the initial conditions and source terms, without extra assumptions on the regularity of the solution. Strong convergence in $L^2(0,T;{\bf L}^2(Ω))$ was proved for the numerical solutions of both ${\bm u}$ and ${\bm H}$ without any mesh restriction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
