A monotone discretization for integral fractional Laplacian on bounded Lipschitz domains: pointwise error estimates under H\"{o}lder regularity

：吴朔男
：2021-10-28 10:00
：腾讯会议号ID：877668330（无密码）

报告人：吴朔男（北京大学）

时  间：10月28日上午10:00

地  点：腾讯会议号ID：877668330（无密码）

内容摘要:

We propose a monotone discretization for the integral fractional Laplace equation on bounded Lipschitz domains with the homogenous Dirichlet boundary condition. The method is inspired by a quadrature-based finite difference method of Huang and Oberman, but is defined on unstructured grids in arbitrary dimensions with a more flexible domain for approximating singular integral. The scale of the singular integral domain not only depends on the local grid size, but also on the distance to the boundary, since the H ̈\"{o}lder coefficient of the solution deteriorates as it approaches the boundary. By using a discrete barrier function that also reflects the distance to the boundary, we show optimal pointwise convergence rates in terms of the H ̈older regularity of the data on both quasi-uniform and graded grids. Several numerical examples are provided to illustrate the sharpness of the theoretical results.

个人简介：

吴朔男分别于2009年和2014年在北京大学数学科学学院获得学士和博士学位，2014年至2018年在美国宾州州立大学进行博士后研究，2018年秋季加入北京大学数学科学学院信息与计算科学系任助理教授。主要研究方向为偏微分方程数值解,研究内容包括：磁流体力学中的磁对流的稳定离散、高阶椭圆型方程的非协调有限元的构造和分析、多相场的建模和计算等。最近在空间分数阶问题的离散和快速求解器上取得进展。研究工作发表在Math. Comp., Numer. Math., SIAM J. Numer. Anal., J. Comput. Phys., Comput. Methods Appl. Mech. Engrg.,Math. Models Methods Appl. Sci.等核心期刊上。

 

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