受国际合作处资助，应数学系吴勃英教授和数学系与数学研究院孟雄副教授邀请，美国布朗大学舒其望教授将于近日来我校进行讲学活动，欢迎感兴趣的师生参加！

报告题目：Entropy stable high order discontinuous Galerkin methods for hyperbolic conservation laws

报告时间：2017年7月20日上午10：00—11：00

报告地点：格物楼522

报告摘要：It is well known that semi-discrete high order discontinuous Galerkin (DG) methods satisfy cell entropy inequalities for the square entropy for both scalar conservation laws and symmetric hyperbolic systems, in any space dimension and for any triangulations. However, this property holds only for the square entropy and the integrations in the DG methods must be exact. It is significantly more difficult to design DG methods to satisfy entropy inequalities for a non-square convex entropy, and / or when the integration is approximated by a numerical quadrature. In this talk, we report on our recent development of a unified framework for designing high order DG methods which will satisfy entropy inequalities for any given single convex entropy, through suitable numerical quadrature which is specific to this given entropy. Our framework applies from one-dimensional scalar cases all the way to multi-dimensional systems of conservation laws. For the one-dimensional case, our numerical quadrature is based on the methodology established in the literature, with the main ingredients being summation-by-parts (SBP) operators derived from Legendre Gauss-Lobatto quadrature, the entropy stable flux within elements, and the entropy stable flux at element interfaces. We then generalize the scheme to two-dimensional triangular meshes by constructing SBP operators on triangles based on a special quadrature rule.  A local discontinuous Galerkin (LDG) type treatment is also incorporated to achieve the generalization to convection-diffusion equations. Numerical experiments will be reported to validate the accuracy and shock capturing efficacy of these entropy stable DG methods. This is a joint work with Tianheng Chen.

报告人简介：

舒其望教授1986年于UCLA数学系获得博士学位，现为美国布朗大学应用数学系Theodore B. Stowell University 教授。舒其望教授长期从事于偏微分方程高阶精度数值方法研究，在加权本质无振荡方法、间断有限元方法、天体物理等领域取得一系列重要成果，在国际著名期刊发表论文300余篇，Google scholar上被引用47377次。舒教授为首届冯康奖获得者、美国工业与应用数学学会首届会士、美国数学会首届会士、世界数学家大会邀请大会报告。