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，美国爱荷华州立大学闫珏副教授将于近日来公司进行讲学活动，欢迎感兴趣的师生参加！

报告题目1：Recent developments on direct discontinuous Galerkin methods

报告时间1：2017年7月17日上午9：00—10：00

报告地点1：格物楼522

报告摘要：We first introduce the direct discontinuous Galerkin (DDG) method and its variations, namely the DDGIC and symmetric DDG methods. Compared to the leading diffusion DG method solvers like the interior penalty method (SIPG), we find out our diffusion solver the DDG methods have many advantages. While the SIPG method needs polynomial degree dependent large enough penalty coefficient to stabilize the scheme, numerically we observe small fixed constant penalty coefficient is enough for the DDGIC method to obtain optimal convergence. Under the topic of maximum principle, DDG methods numerical solution can be proved to satisfy strict maximum principle even on unstructured triangular meshes with at least third order of accuracy.

报告题目2：Direct discontinuous Galerkin methods for Keller-Segel Chemotaxis equations

报告时间2：2017年7月18日上午9：00—10：30

报告地点2：格物楼503

报告摘要：We develop a new direct discontinuous Galerkin (DDG) methods to solve Keller-Segel Chemotaxis equations. Different to available DG methods or other numerical methods in literature, we introduce no extra variable to approximate the chemical density gradients but solve the system directly. With P^k polynomial approximations, we observe no order loss and optimal (k+1)th order convergence is obtained. The reason that DDG methods is convergent with optimal orders is that DDG methods have the super convergence property on its approximating to solution gradients. With Fourier (Von Neumann) analysis technique, we prove the DDG solution’s spatial derivative is super convergent with at least (k+1)th order under moment norm. We show the cell density approximations are strictly positive with at least third order of accuracy. We also carry out second order finite difference schemes to simulate the liquid and semi-solid models of chemotaxis. The pattern formations observed are consistent to those in literature. 

报告人简介：

闫珏副教授在1995年和1998年于吉林大学数学系分别获得学士和硕士学位，2002年于布朗大学应用数学系获得博士学位，现为美国爱荷华州立大学副教授。闫珏副教授长期致力于流体力学方程的高阶精度数值方法及其应用研究，在非线性色散波方程、哈密尔顿-雅克比方程、直接间断有限元方法、气体动力学方程组的保正算法及界面捕捉的水平集方法等领域取得大量重要成果。闫珏副教授主持美国国家自然科学基金2项，发表包含SIAM Journal on Numerical Analysis、Journal of Computational Physics、Journal of Scientific Computing在内的高水平论文20余篇。