Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
邹青松 教授, 中山大学数学与计算科学学院
Inviter:
毛士鹏
Title:
High order continuous local-conserving fluxes and finite-volume-like finite element solutions for elliptic equations
Time & Venue:
2018.2.2 15:00-16:30 Z311
Abstract:
In the first part of the talk, we will first give a brief review on our recent advances on the theoretical analysis of high order finite volume element method. In the second part, we derive a high order globally continuous and locally conservative flux field and a high order finite-volume-like solution from the continuous Galerkin (CG) finite element solution. The main idea is to post-process the CG solution by solving a small linear algebraic system on each element of the underlying mesh. Both the post-processed flux field and the finite-volume-like solution satisfy the conservation law on each {\it control volume} of the {\it dual mesh}. Moreover, both the post-processed flux field and the gradient of finite-volume-like solution converge to the exact flux with optimal convergence rates.