题  目：An adaptive finite element DtN method for the transmission problem

内容简介：In this talk, I will consider the scattering of a time-harmonic acoustic incident wave by a bounded penetrable obstacle, which is immersed in a homogeneous compressible air/fluid. Based on a Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition is introduced and the model is formulated as a transmission boundary value problem. By a new duality argument technique, an a posteriori error estimate is derived for the finite element method with the truncated DtN boundary operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of the DtN boundary operator, where the latter decays exponentially with respect to the truncation parameter. An adaptive finite element algorithm is proposed for solving the transmission problem, where the truncation parameter is determined through the truncation error and the mesh elements for local refinements are chosen through the finite element discretization error. Numerical experiments are presented to demonstrate 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SIAM J. Numer. Anal.，Math. Comput.，J.Sci. Comput.以及IMA J. 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