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.
翻译:我们提出并分析固定式压缩磁力动力学方程式的混合高序(HHO)计划。该计划有任意的精确顺序,适用于通用多面体模类。对于足够小的来源,我们证明速度和磁场的能源标准估计有误,压力估计有误2美元;这些估计对于小面孔是完全可靠的,对于网状尺寸是最佳的。使用紧凑技术,我们还证明该计划与持续问题的解决一致,而不论来源大小。最后,我们通过对四面体和Voronoimesh家族的3D数字测试来说明我们的理论结果。