In this paper, we study some techniques for solving numerically magnetostatic systems. We consider fairly general assumptions on the magnetic permeability tensor. It is elliptic, but can be nonhermitian. In particular, we revisit existing classical variational methods and propose new numerical methods. The numerical approximation is either based on the classical edge finite elements or on continuous Lagrange finite elements. For the first type of discretization, we rely on the design of a new, mixed variational formulation that is obtained with the help of T-coercivity. The numerical method can be related to a perturbed approach for solving mixed problems in electromagnetism. For the second type of discretization, we rely on an augmented variational formulation obtained with the help of the weighted regularization method.

在本文中，我们研究了一些求解数值静磁系统的技术。我们考虑对磁导率张量的相当普遍的假设。它是椭圆形的，但可以是非埃尔米特式的。特别是，我们重新审视现有的经典变分方法并提出新的数值方法。数值近似基于经典边缘有限元或连续拉格朗日有限元。对于第一种类型的离散化，我们依靠在T矫顽力的帮助下获得的新的混合变分公式的设计。数值方法可以与解决电磁学混合问题的扰动方法相关。对于第二种类型的离散化，我们依靠借助加权正则化方法获得的增强变分公式。