报告题目：Time-stepping for Volterra integro-differential equations based on the discontinuous Galerkin method

报告人：Hermann Brunner

Department ofMathematicsHong KongBaptistUniversityand Department of Mathematics andStatisticsMemorialUniversityofNewfoundland

时间：2012年11月16日（星期五）10:00-11:00

地点：理科楼数学系A304

摘要：The analysis of discontinuous Galerkin (DG) time-stepping methods for ordinary and (parabolic) partial differential equations dates back to the early 1970s and mid-1980s, respectively, and their $hp$-versions were introduced in 2000. For ordinary Volterra integro-differential equations (including problems with non-smooth solutions) these methods were first studied in 2006.

In this talk I shall briefly review the development of DG and related collocation methods and then describe recent results (obtained jointly with D. Schotzau and K. Mustapha) on the convergence analysis of $hp$-DG time-stepping methods for ordinary and parabolic Volterra integro-differential equations. It will also be shown that a number of important problems remain to be addressed, for example the derivation of a posteriori (computable) error estimates and the convergence analysis for the $hp$-version of collocation time-stepping methods.

报告人简介：Hermman Brunner教授是积分-微分方程领域的著名专家，在积分-微分方程的理论和数值解的研究方面做出了很多开创性的工作。是SIAM Journal on Numerical Analysis IMA Journal of Numerical Analysis和Journal of Integral Equations and Applications等学术期刊的编委。现任Atlantic Association for Research in the Mathematical Sciences的主席。

联系人：殷东生