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学术预告-Lowest-order Weak Galerkin (WG) FEMs for Elliptic and Elastic Equations on General Polygonal Meshes

发布时间: 2018-06-29 15:31:41   作者:本站编辑   来源: 本站原创   浏览次数:

讲座主题:Lowest-order Weak Galerkin (WG) FEMs for Elliptic and Elastic Equations on General Polygonal Meshes

专家姓名:刘江国

工作单位:科罗拉多州立大学

讲座时间:2018年7月2日10:00

讲座地点:数学院大会议室

主办单位:今期东方心经马报图l数学与信息科学学院

内容摘要:

    This talk presents the lowest-order weak Galerkin (WG) finite element method for Darcy flow or elliptic boundary value problems on general convex polygonal meshes. In this approach, constants are used in element interiors and on edges to approximate the primal variable (pressure). The discrete weak gradients of these constant basis functions are established in simple H(div)-subspaces on polygons that are explicitly constructed by using the normalized coordinates and Wachspress coordinates. These discrete weak gradients are used to approximate the classical gradient in the variational form. No penalization is needed for this new method.  The method results in symmetric positive-definite sparse linear systems. It is locally mass-conservative, and produces continuous normal fluxes. The new method has optimal-order convergence in pressure (primal variable), velocity, and normal flux, when the convex polygon meshes are shape-regular.  Extension to planar elasticity is also discussed.

主讲人介绍:

    刘江国,美国科罗拉多州立大学学教授、博士生导师、国际SCI期刊《Journal of Computational and Applied Mathematics》 副主编,SIAM Central States Section President,已发表学术论文40余篇,主持多项美国国家自然科学基金。


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