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：本文提出并分析了一种用于稳态不可压缩磁流体动力学方程的混合高阶（HHO）格式。该格式具有任意阶精度，适用于通用多面体网格。对于足够小的源项，我们证明了速度和磁场在能量范数下、以及压力在$L^2$范数下的误差估计；这些估计在涉及小面时完全鲁棒，且关于网格尺寸具有最优阶。利用紧性技巧，我们还证明了无论源项大小，该格式均收敛至连续问题的解。最后，我们通过四面体和Voronoi网格系列上的三维数值实验验证了理论结果。