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.
翻译:Galerkin (DG) 方法是通常的 Galerkin 定点元素方法的延伸, 虽然对 DG 方法进行了大量研究, 但大多数方法都假定了线状金属的形状常规性条件, 以便进行理论错误分析和实际计算。 在本文中, 我们提出了一个新的对称内部惩罚DG 方法, 并修改了惩罚期限。 我们显示, 新的DG 方案在不给系状金属施加形状常规性条件的情况下, 继承了标准 DG 方法的所有良好特性, 因而对厌食类草木具有很强的特性。 数字实验证实了所获得的理论错误估计值 。