论文标题
浸入多边形网格上的椭圆界面问题的弱弱GALERKIN方法
An Immersed Weak Galerkin Method for Elliptic Interface Problems on Polygonal Meshes
论文作者
论文摘要
在本文中，我们提出了一种沉浸式弱的彩色方法，用于在多边形网格上求解二阶椭圆界面问题，其中网格不需要与界面对齐。离散空间由每个边缘上的常数组成，损坏的线性多项式满足每个元素中的界面条件。对于三角形网格，这种断裂的线性plyNomials与浸入有限元方法中的基础函数相吻合[26]。我们建立了损坏的线性多项式的一些近似特性，以及在多边形网格上溶液的一定投影的离散弱梯度。然后，在确切解决方案的某些假设下，我们在离散的$ h^1 $ -seminorm中证明了我们方案的最佳误差估计。提供数值实验以确认我们的理论分析。
In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on each edge and broken linear polynomials satisfying the interface conditions in each element. For triangular meshes, such broken linear plynomials coincide with the basis functions in immersed finite element methods [26]. We establish some approximation properties of the broken linear polynomials and the discrete weak gradient of a certain projection of the solution on polygonal meshes. We then prove an optimal error estimate of our scheme in the discrete $H^1$-seminorm under some assumptions on the exact solution. Numerical experiments are provided to confirm our theoretical analysis.
