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.

中文翻译：

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强各向异性扩散方程的高效高阶数值求解器

在本文中，我们提出了一种内部惩罚不连续伽辽金有限元方案，用于解决聚变应用中磁化等离子体中产生的具有强各向异性的扩散问题。我们证明了高阶方案产生的精度，并开发了一种有效的预处理技术来解决相应的线性系统，该技术对问题的网格尺寸和各向异性具有鲁棒性。提供了几个数值测试来验证所提出算法的准确性和效率。