We propose and analyze two convection quasi-robust and pressure robust finite element methods for a fully nonlinear time-dependent magnetohydrodynamics problem. The schemes make use of suitable upwind and CIP stabilizations to handle the fluid and magnetic convective terms. The developed error estimates are uniform in both diffusion parameters and optimal with respect to the diffusive norm; furthermore, for the second (more complex) method we are able to show a quicker error reduction rate in convection dominated regimes. A set of numerical tests support our theoretical findings.

翻译：针对完全非线性时变磁流体动力学问题，我们提出并分析了两种对流准稳健与压强稳健的有限元方法。这两种方案采用合适的迎风稳定化与CIP稳定化技术处理流体和磁场的对流项。所建立的误差估计关于扩散参数一致，且在扩散范数下具有最优性；此外，对于第二种（更复杂的）方法，我们证明了对流主导区域中更快的误差衰减率。一系列数值实验验证了我们的理论结果。