講座主題：Lowest-order Weak Galerkin (WG) FEMs for Elliptic and Elastic Equations on General Polygonal Meshes
專家姓名：劉江國
工作單位：科羅拉多州立大學
講座時間：2018年7月2日10:00
講座地點：數學院大會議室
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
劉江國，美國科羅拉多州立大學學教授、博士生導師、國際SCI期刊《Journal of Computational and Applied Mathematics》 副主編，SIAM Central States Section President，已發表學術論文40余篇，主持多項美國國家自然科學基金。
