Polygonal staggered discontinuous Galerkin methods
Abstract
In this talk, I will introduce the recently-devised staggered discontinuous Galerkin (DG) methods with extensive applications to various partial differential equations. A class of locally conservative, lowest order staggered discontinuous Galerkin methods on general polygonal meshes for elliptic equations are proposed. An adaptive mesh re-finement algorithm guided by a rigorous a posteriori error estimator on the polygonal meshes will be introduced. This adaptive mesh refinement algorithm is advantageous in the sense that it can handle arbitrary shapes of polygon, and hanging nodes can be naturally incorporated into the construction ofthe method. The numerical experiments confirm the good performances of the proposed method. Some applications of high order staggered DG methods to pseudostress velocity formulation of Stokes equations and single phase flow in fractured porous media will also be introduced, in which several numerical experiments including unfitted meshes will be displayed. This isjoint work with Eun-Jae Park at Yonsei University, South Korea and Eric Chung at theChineseUniversityofHongKong,HongKong,China.
Registration URL
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