题 目：Anadaptive finite element DtN method for the transmission problem
内容简介：Inthis talk, I will consider the scattering of a time-harmonic acousticincident wave by a bounded penetrable obstacle, which is immersed ina homogeneous compressible air/fluid. Based on a Dirichlet-to-Neumann(DtN) operator, an exact transparent boundary condition is introducedand the model is formulated as a transmission boundary value problem.By a new duality argument technique, an a posteriori error estimateis derived for the finite element method with the truncated DtNboundary operator. The a posteriori error estimate consists of thefinite element approximation error and the truncation error of theDtN boundary operator, where the latter decays exponentially withrespect to the truncation parameter. An adaptive finite elementalgorithm is proposed for solving the transmission problem, where thetruncation parameter is determined through the truncation error andthe mesh elements for local refinements are chosen through the finiteelement discretization error. Numerical experiments are presented todemonstrate the effectiveness of the proposed method.
报告人：吕俊良
报告人简介：吉林大学数学学院，教授，博导。研究兴趣包括无界域散射问题的数值方法，反散射问题的数值算法与理论，偏微分方程有限体积元法等。研究成果发表在SIAMJ. Numer. Anal.，Math.Comput.，J.Sci.Comput.以及IMAJ. Numer. Anal.等杂志上。承担国家自然科学基金项目、国防项目、吉林省自然科学基金等。
现任中国数学会计算数学分会理事、中国仿真学会仿真算法专委会委员、吉林省数学会理事、美国数学会数学评论员。
时 间：2023年11月15日（周三）下午15：00开始
地 点：腾讯会议：194-276-676
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2023年11月14日
