The numerical simulation of the equilibrium of the plasma in a tokamak as well as its self-consistent coupling with resistive diffusion should benefit from higher regularity of the approximation of the magnetic flux map. In this work, we propose a finite element approach on a triangular mesh of the poloidal section, that couples piece-wise linear finite elements in a region that does not contain the plasma and reduced Hsieh-Clough-Tocher finite elements elsewhere. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details in the rest of the computational domain. The continuity of the numerical solution at the coupling interface is weakly enforced by mortar projection. A new technique for the computation of the geometrical coefficients is also presented.

托卡马克中的等离子体平衡及其与电阻扩散的自洽耦合的数值模拟应受益于磁通量图逼近的较高规律性。在这项工作中，我们提出了一种在极向截面的三角形网格上的有限元方法，该方法将不包含等离子体的区域中的分段线性有限元与其他地方的Hsieh-Clough-Tocher有限元简化了耦合。这种方法提供了灵活性，可以轻松地以低成本实现较高等阶的规则性，以近似等离子覆盖的域中的磁通函数，同时在其余计算域中保留几何细节的精确网格划分。砂浆投影弱地增强了耦合界面处数值解的连续性。