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学术报告-谢小平

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2020-11-13 16:29:00

学术报告


题      目:An eXtended HDG method for Darcy-Stokes-Brinkman interface problems



报  告  人:谢小平   教授  (邀请人:钟柳强 )

                                   四川大学




时      间:2020-11-13 11:00--11:50


地      点:学院401


报告人简介:

        谢小平,四川大学数学学院、长江数学中心的教授、博士生导师,四川省学术和技术带头人,教育部新世纪优秀人才,德国洪堡学者。研究方向为偏微分方程数值解、有限元法。现兼任中国工业与应用数学学会油水资源数值方法专业委员会副主任委员,中国工业与应用数学学会高性能计算与数学软件专业委员会委员,中国仿真学会集成微系统建模与仿真专业委员会委员。 期刊《Numerical Analysis and Applicable Mathematics》、《计算数学》和《高等学校计算数学学报》编委。第八届世界华人数学家大会(ICCM2019)45分钟报告人。

摘      要:

       We propose an interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin(X-HDG) method for Darcy-Stokes-Brinkman interface problems in two and three dimensions. The method uses piecewise linear polynomials for the velocity approximation and piecewise constants for both the velocity gradient and pressure approximations in the interior of elements inside the subdomains separated by the interface, and uses piecewise constants for the numerical traces of velocity on the inter-element boundaries inside the subdomains as well as on the interface. Optimal error estimates are derived in the piecewise $H^1$-norm for the velocity and in the $L^2$-norm for the velocity and pressure. Numerical experiments confirm the theoretical results.