论文标题
各向异性网状的强大不连续的盖尔金方案
A robust discontinuous Galerkin scheme on anisotropic meshes
论文作者
论文摘要
不连续的Galerkin（DG）方法是通常的Galerkin有限元方法的扩展。尽管关于DG方法的研究大量研究，但其中大多数都假定了在网格上进行理论误差分析和实际计算的形状定型条件。在本文中，我们提出了一个新的对称内部惩罚DG计划，并带有修改后的罚款。我们表明，新的DG方案在网格上施加了形状的定型条件，而是继承了标准DG方法的所有良好特性，因此在各向异性网格上具有鲁棒性。数值实验证实了获得的理论误差估计值。
Discontinuous Galerkin (DG) methods are extensions of the usual Galerkin finite element methods. Although there are vast amount of studies on DG methods, most of them have assumed shape-regularity conditions on meshes for both theoretical error analysis and practical computations. In this paper, we present a new symmetric interior penalty DG scheme with a modified penalty term. We show that, without imposing the shape-regularity condition on the meshes, the new DG scheme inherits all of the good properties of standard DG methods, and is thus robust on anisotropic meshes. Numerical experiments confirm the theoretical error estimates obtained.
