j9九游会

报告主题：PDE的Weak Galerkin 要领的新效果
报告人：刘江国 教授 (Colorado State University)
报告时间：2017年5月31日（周三）14:00
报告所在：校本部G507
约请人：马清静
主理部分：理学院数学系

报告摘要：In this talk, we present new ideas of weak Galerkin (WG) finite element methods for solving the Darcy and elasticity equations. Given a mesh, the WG methodology sets basis functions in element interiors and edges/faces and establishes (through integration by parts) discrete weak gradient or divergence or curl in certain spaces that have desired approximation capacity. The WG approach offers also nice properties, e.g., local mass conservation and flux normal continuity for Darcy flow and locking-free for elasticity. For the Darcy equation in 2-dim, we develop the lowest order WG finite element method that utilizes constant approximants for pressure but specifies their discrete weak gradients in Raviart-Thomas spaces. This particular method treats triangular, rectangular, and quadrilateral meshes in a unified approach and attains optimal-order convergence in pressure, velocity, and flux. Similarly, constant vector approximants can be used in element interiors and edges/faces for solving the linear elasticity equation in 2-dim or 3-dim, whereas first order accuracy are obtained for displacement, stress, and dilation.

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