Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
吴朔男 助理教授,北京大学
Inviter:
张硕 副研究员
Title:
Simplex-averaged finite element methods for H(grad), H(curl) and H(div) convection-diffusion problems
Time & Venue:
2018.12.7 10:00-11:00 Z311
Abstract:
In this talk, we construct and analyze a finite element approximation for the $H(D)$ convection-diffusion problem where $D$ can be chosen as $, $ or $ in 3D case. An essential feature of these constructions is to properly average the PDE coefficients on the sub-simplexes. The schemes are of the class of exponential fitting methods that result in special upwinding schemes when the diffusion coefficient approaches to zero. Their well-posedness are established for sufficiently small mesh size assuming that the convection-diffusion problems are uniquely solvable. Convergence of first order is derived under minimal smoothness of the solution. Some numerical examples are given to demonstrate the robustness and effectiveness for general convection-diffusion problems.