In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. We demonstrate the accuracy produced by the high-order scheme and develop an efficient preconditioning technique to solve the corresponding linear system, which is robust to the mesh size and anisotropy of the problem. Several numerical tests are provided to validate the accuracy and efficiency of the proposed algorithm.

翻译：在本文中,我们提出了一个内部惩罚不连续的Galerkin有限元素计划,用于解决磁化等离子体在聚变应用中产生的强烈厌异性扩散问题,我们展示了高级计划产生的准确性,并开发了一种有效的先决条件技术来解决相应的线性系统,这个系统与问题的网目尺寸和厌异性相当强。我们提供了若干数字测试,以验证提议的算法的准确性和效率。