In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in space-time domain. Based on the Babu\v{s}ka--Ne\v{c}as theory we prove unique solvability both for the continuous variational formulation and for a standard Galerkin finite element discretization in the space-time domain. This approach allows for an adaptive resolution of the solution both in space and time, but it requires the solution of the overall system of algebraic equations. While the use of parallel solution algorithms seems to be mandatory, this also allows for a parallelization simultaneously in space and time. This approach is used for the eddy current approximation of the Maxwell equations which results in an elliptic-parabolic interface problem. Numerical results for linear and nonlinear constitutive material relations confirm the applicability, efficiency and accuracy of the proposed approach.

翻译：本文提出并分析了一种用于旋转电机数值模拟的时空有限元方法，其中有限元网格固定在时空域内。基于Babuška–Nečas理论，我们证明了连续变分公式和标准Galerkin有限元离散在时空域中的唯一可解性。该方法允许在空间和时间上对解进行自适应细化，但需要求解整体代数方程组。尽管使用并行求解算法似乎是必要的，但这也同时实现了空间和时间上的并行化。该方法用于麦克斯韦方程组的涡流近似，从而形成椭圆-抛物型界面问题。线性和非线性本构关系的数值结果验证了所提方法的适用性、效率和精度。