报告人：李小林（重庆师范大学）

时间：2024年03月15日 10:30-

地址：理科楼LA106

摘要：Numerical integration poses greater challenges in Galerkin meshless methods than finite element methods (FEMs) owing to the non-polynomial feature of meshless shape functions. The reproducing kernel gradient smoothing integration (RKGSI) is one of the optimal numerical integration techniques in Galerkin meshless methods with minimum integration points.

In this report, the effect of the RKGSI on the element-free Galerkin (EFG) method is studied for elliptic boundary value problems with mixed boundary conditions of Dirichlet and Robin type. Theoretical results of smoothed gradients in the RKGSI such as properties and error estimations are provided. Fundamental criteria on how to determine integration points and weights of quadrature rules are established according to necessary algebraic precision. By using the Nitsche’s technique to impose Dirichlet boundary condition, the existence, uniqueness and error estimations of the solution of the EFG method with numerical integration are analyzed. The theoretical error estimation indicates how to choose quadrature rules to recover the optimal convergence rate.

简介：李小林，博士，教授，博士生导师。2005年7月本科毕业于太阳成集团数学与应用数学系，2009年6月博士毕业于太阳成集团计算数学专业，然后至今在重庆师范大学工作。研究领域为计算数学，研究方向为微分方程数值解法，研究成果获得了重庆市十佳科技青年奖1项、重庆市自然科学奖二等奖和三等奖各1项。入选重庆市特支计划青年拔尖人才、重庆英才创新创业领军人才、重庆市巴渝学者特聘教授，主持了重庆市杰出青年科学基金和4项国家自然科学基金项目。

邀请人：王坤

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