Speaker
Dr. Qingguang Guan, Assistant Professor, University of Southern Mississippi
Title
Mathematics Seminar Series
Subtitle
“Weak Galerkin Method with General-Shape Elements for Second-Order Problems
Digital Location
https://msstate.webex.com/msstate/j.php?MTID=m639ad6f48c2366d139bcadf4ff99aa15
Abstract: The weak Galerkin method as a new variation of the finite element methods has been applied to solving various partial differential equations, it has main advantages in using discontinuous basis functions, keeping mass conservation, producing continuous numerical flux, and employing elements as polygons/polyhedrons. In this talk, we relax the shape-regular requirement, design new basis functions for the weak Galerkin method, and use (1) polytopal elements with small edges/faces and (2) curvilinear polytopal elements to solve the elliptic and interface problems with Lipschitz continuous curved boundaries/interfaces. Arbitrary high-order and optimal convergence rates are obtained theoretically. Numerical results validate our findings.
For more information, please contact: Dr. Vu Thai Luan (luan@math.msstate.edu).