论文标题
用于固定的，不可压缩的磁性水力学方程的混合高阶方案
A hybrid high-order scheme for the stationary, incompressible magnetohydrodynamics equations
论文作者
论文摘要
我们提出和分析了一种固定不可压缩磁性流体动力学方程的混合高阶（HHO）方案。该方案具有任意的准确性顺序，并且适用于通用的多面体网格。对于足够小的来源，我们证明了速度和磁场的能量规范的错误估计，以及压力的$ l^2 $ norm；这些估计值相对于小面完全健壮，并且相对于网格大小的最佳顺序。使用紧凑性技术，我们还证明该方案会收敛到连续问题的解决方案，而与源相关的问题是小还是大。最后，我们通过对四面体和伏诺诺网格家族的3D数值测试来说明我们的理论结果。
We propose and analyse a hybrid high-order (HHO) scheme for stationary incompressible magnetohydrodynamics equations. The scheme has an arbitrary order of accuracy and is applicable on generic polyhedral meshes. For sources that are small enough, we prove error estimates in energy norm for the velocity and magnetic field, and $L^2$-norm for the pressure; these estimates are fully robust with respect to small faces, and of optimal order with respect to the mesh size. Using compactness techniques, we also prove that the scheme converges to a solution of the continuous problem, irrespective of the source being small or large. Finally, we illustrate our theoretical results through 3D numerical tests on tetrahedral and Voronoi mesh families.
