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A Discontinuous Galerkin Method by Patch Reconstruction for Elliptic Interface Problem on Unfitted Mesh
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2020-04-30 , DOI: 10.1137/19m1290528 Ruo Li , Fanyi Yang
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2020-04-30 , DOI: 10.1137/19m1290528 Ruo Li , Fanyi Yang
SIAM Journal on Scientific Computing, Volume 42, Issue 2, Page A1428-A1457, January 2020.
We propose a discontinuous Galerkin (DG) method to approximate the elliptic interface problem on unfitted mesh using a new approximation space. The approximation space is constructed by patch reconstruction with one degree of freedom per element. The optimal error estimates in both the $L^2$ norm and the DG energy norm are obtained, without restrictions on how the interface intersects the elements in the mesh. The stability near the interface is ensured by the patch reconstruction and no special numerical flux is required. The convergence order by numerical results in both two and three dimensions agrees with the error estimates perfectly. More than enjoying the advantages of the DG method, the new method may achieve even better efficiency in number of degrees of freedom than the conforming finite element method as illustrated by our numerical examples.
中文翻译：
不匹配网格上椭圆界面问题的不连续Galerkin补丁重构方法
SIAM科学计算杂志，第42卷，第2期，第A1428-A1457页，2020年1月。
我们提出了一种不连续Galerkin（DG）方法，以使用新的近似空间来近似非拟合网格上的椭圆界面问题。近似空间是通过面片重构以每个元素一个自由度来构造的。可以在$ L ^ 2 $范数和DG能量范数中获得最佳误差估计，而对界面与网格中元素的相交方式没有限制。贴片重建可确保界面附近的稳定性，并且不需要特殊的数值通量。二维和三维数值结果的收敛阶与误差估计完全吻合。除了享受DG方法的优势外，
更新日期：2020-04-30
We propose a discontinuous Galerkin (DG) method to approximate the elliptic interface problem on unfitted mesh using a new approximation space. The approximation space is constructed by patch reconstruction with one degree of freedom per element. The optimal error estimates in both the $L^2$ norm and the DG energy norm are obtained, without restrictions on how the interface intersects the elements in the mesh. The stability near the interface is ensured by the patch reconstruction and no special numerical flux is required. The convergence order by numerical results in both two and three dimensions agrees with the error estimates perfectly. More than enjoying the advantages of the DG method, the new method may achieve even better efficiency in number of degrees of freedom than the conforming finite element method as illustrated by our numerical examples.
中文翻译：
不匹配网格上椭圆界面问题的不连续Galerkin补丁重构方法
SIAM科学计算杂志，第42卷，第2期，第A1428-A1457页，2020年1月。
我们提出了一种不连续Galerkin（DG）方法，以使用新的近似空间来近似非拟合网格上的椭圆界面问题。近似空间是通过面片重构以每个元素一个自由度来构造的。可以在$ L ^ 2 $范数和DG能量范数中获得最佳误差估计，而对界面与网格中元素的相交方式没有限制。贴片重建可确保界面附近的稳定性，并且不需要特殊的数值通量。二维和三维数值结果的收敛阶与误差估计完全吻合。除了享受DG方法的优势外，
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