论文标题
一种新的原始双二重弱彩色方法，用于椭圆界面问题，具有低规律性假设
A New Primal-Dual Weak Galerkin Method for Elliptic Interface Problems with Low Regularity Assumptions
论文作者
论文摘要
本文介绍了一个新的原始双二重弱伽勒素（PDWG）有限元方法，用于在精确解决方案以及接口和边界数据上具有超低规律性假设的二阶椭圆界面问题。事实证明，PDWG方法在离散和Sobolev规范中具有最佳的错误估计顺序稳定且准确。特别是，对于精确解决方案$ u $的$δ> \ frac12 $，在$ u \ in h^δ（ω）$的低规律性假设下得出了错误估计。进行了广泛的数值实验，以提供数值解决方案来验证新PDWG方法的效率和准确性。
This article introduces a new primal-dual weak Galerkin (PDWG) finite element method for second order elliptic interface problems with ultra-low regularity assumptions on the exact solution and the interface and boundary data. It is proved that the PDWG method is stable and accurate with optimal order of error estimates in discrete and Sobolev norms. In particular, the error estimates are derived under the low regularity assumption of $u\in H^δ(Ω)$ for $δ> \frac12$ for the exact solution $u$. Extensive numerical experiments are conducted to provide numerical solutions that verify the efficiency and accuracy of the new PDWG method.
