• 论文 •

### 曲边区域上的多边形网格间断有限元离散及其多重网格算法

1. 南京师范大学数学科学学院, 南京 210023
• 收稿日期:2021-03-24 出版日期:2022-07-14 发布日期:2022-08-03

Liu Yi, Wang Yanqiu. POLYGONAL DISCONTINUOUS GALERKIN METHODS ON CURVED REGIONS AND ITS MULTIGRID PRECONDITIONER[J]. Mathematica Numerica Sinica, 2022, 44(3): 396-421.

### POLYGONAL DISCONTINUOUS GALERKIN METHODS ON CURVED REGIONS AND ITS MULTIGRID PRECONDITIONER

Liu Yi, Wang Yanqiu

1. School of Mathematics Science, Nanjing Normal University, Nanjing 210023, China
• Received:2021-03-24 Online:2022-07-14 Published:2022-08-03

The main purpose of this paper is to study the discontinuous Galerkin discretization of second-order elliptic partial differential equations on curved regions. We use multiple short edges to approximate the curved boundary and achieve the optimal convergence order in H1 norm for high-order elements. This method is also applied to the interface problem with curved interfaces and obtains the optimal convergence of high-order elements. Furthermore, we prove that the W-cycle and V-cycle multigrid preconditioners converge uniformly provided that the number of smoothing is sufficiently large. Finally, numerical results are presented to verify the correctness of the theoretical results.

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