论文标题
椭圆形界面问题的混合有限差方案，出现不连续和高对比度系数的问题
Hybrid Finite Difference Schemes for Elliptic Interface Problems with Discontinuous and High-Contrast Variable Coefficients
论文作者
论文摘要
对于不连续系数的椭圆界面问题，不规则点中紧凑的9分差差方案的最大精度订单为三个[7]。不连续的系数通常在逼真的问题的多孔介质中突然在界面曲线上突然跳跃，从而导致数值方法的污染效应。因此，为了获得上述问题的合理数值解决方案，必须使用高阶方案及其有效实施。在本文中，我们提出了一种有效且灵活的方式，以实现混合动力（9点方案（9点方案）内部常规点的第六级准确性和13分方案，具有第五级级的准确性，用于内部不规则点的准确性）在均匀的网格中，对于椭圆界面的均匀差异方案，椭圆界面问题不连续和高分子的平滑coffercy $ $ $ $ $ $ $。我们还以均匀网格的价格得出了$ 6 $ - 点和$ 4 $ - 点有限差方案，在矩形中的各种混合边界条件（dirichlet，neumann and neumann and robin）的侧点和角点的第六级准确性。我们的数值实验证实了$ l_2 $和$ l _ {\ infty} $规范的灵活性和第六订单精度。
For elliptic interface problems with discontinuous coefficients, the maximum accuracy order for compact 9-point finite difference scheme in irregular points is three [7]. The discontinuous coefficients usually have abrupt jumps across the interface curve in the porous medium of realistic problems, causing the pollution effect of numerical methods. So, to obtain a reasonable numerical solution of the above problem, the higher order scheme and its effective implementation are necessary. In this paper, we propose an efficient and flexible way to achieve the implementation of a hybrid (9-point scheme with sixth order accuracy for interior regular points and 13-point scheme with fifth order accuracy for interior irregular points) finite difference scheme in uniform meshes for the elliptic interface problems with discontinuous and high-contrast piecewise smooth coefficients in a rectangle $Ω$. We also derive the $6$-point and $4$-point finite difference schemes in uniform meshes with sixth order accuracy for the side points and corner points of various mixed boundary conditions (Dirichlet, Neumann and Robin) of elliptic equations in a rectangle. Our numerical experiments confirm the flexibility and the sixth order accuracy in $l_2$ and $l_{\infty}$ norms of the proposed hybrid scheme.
