报告题目：椭圆界面问题的鲁棒高效间断Galerkin方法

Robust and efficient discontinuous Galerkin methods for elliptic interface problems

报 告人：朱江 研究员

时 间： 9月17日（周四）下午2:00-4:00

地 点：文理楼254报告厅

报告摘要：Because of the discontinuity of the interface problems, it is natural to apply the discontinuous Galerkin (DG) finite element methods to solve those problems. In this talk, both fitted and unfitted mixed hybrid discontinuous Galerkin (MHDG) finite element methods are proposed to solve the elliptic interface problems. For the fitted case, the diffusion and convection-diffusion problems are solved directly by MHDG method. For the unfitted case, the broken basis functions (unnecessary to satisfy the jump conditions) are introduced to those elements which are cut across by interface, the weights depending on the volume fractions of cut elements and the different diffusions (or material heterogeneities) are used to stabilize the method, and the idea of the Nitsche s penalty method is applied to guarantee the jumps on the interface parts of cut elements. Unlike the immersed interface finite element methods (IIFEM), the two jump conditions are enforced weakly in our variational formulations. So, our unfitted interface MHDG method can be applied more easily than IIFEM to general cases, particularly when the immersed basis function cannot be constructed. Numerical results on convergence and sensitivities of both interface location within a cut element and material heterogeneities show that the proposed methods are robust and efficient for interface problems.

报告人简介：朱江，巴西国家科学计算实验室研究员、博士生导师，加拿大Alberta大学、中科院及山东大学等客座教授。主要从事计算数学及计算力学领域的研究，尤其在非线性热耦合问题的数学及数值分析方面，取得一系列成果。目前担任国际期刊《International Journal of Numerical Analysis and Modeling B》的 编委。迄今已在《SIAM Journal on Numerical Analysis》, 《Computer Methods in Applied Mechanics and Engineering》, 《Journal of Computational Physics》等国际顶级期刊发表论文70余篇，承担巴西国家科学基金项目多项。

     理学院 科技处 国际合作与交流处

     2015-09-10