论文标题
二阶椭圆方程的内部过度富集的富含galerkin方法
Interior over-penalized enriched Galerkin methods for second order elliptic equations
论文作者
论文摘要
在本文中，我们提出了一种富集的Galerkin方法，用于二阶椭圆方程，内部跳跃术语过度元素。具有内部过度化的双线性形式给出了一个非标准的标准，该标准与经典不连续的Galerkin方法中的离散能量标准不同。尽管如此，我们证明，可以通过结合先验和后验误差分析技术来获得最佳的先验误差估计。我们还表明，内部过度占地对于通过分析双线性形式的光谱等效性来构建预处理的预处理是有利的。包括数值结果以说明收敛性和预处理结果。
In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-penalization of interior jump terms. The bilinear form with interior over-penalization gives a non-standard norm which is different from the discrete energy norm in the classical discontinuous Galerkin methods. Nonetheless we prove that optimal a priori error estimates with the standard discrete energy norm can be obtained by combining a priori and a posteriori error analysis techniques. We also show that the interior over-penalization is advantageous for constructing preconditioners robust to mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical results are included to illustrate the convergence and preconditioning results.
