报告题目：A CIP-FEM for high-frequency scattering problem with the truncated DtN boundary condition

报告时间：2020年12月25日（星期五） 上午9:00 - 10:30

报告地点：数学与统计学院310会议室

报告人： 郑伟英 研究员（中国科学院数学与系统科学研究院）

摘要：A continuous interior-penalty finite element method (CIP-FEM) is proposed to solve high-frequency Helmholtz scattering problems by an impenetrable obstacle in two dimensions. To formulate the problem on a bounded domain, a DtN boundary condition is proposed on the outer boundary by truncating the Fourier series of the original DtN mapping into finite terms. Assuming the truncation order N>kR, the H^j-stabilities, j=0,1,2, are established for both forward and dual problems, with explicit and sharp estimates of the upper bounds with respect to the wave number k. Under the condition that k^3h^2 is sufficiently small, we prove that the preasymptotic error estimates for the linear CIP-FEM as well as the linear continuous FEM are C(kh+k^3h^2). Numerical experiments are presented to validate the theoretical results.

报告人简介：郑伟英，中科院数学与系统科学研究院研究员。1996年于郑州大学获学士学位，2002年于北京大学获博士学位，2006-2007年为德国慕尼黑科技大学洪堡基金访问学者，2017年获杰出青年科学基金资助，2019年被聘为中科院数学与系统科学研究院“冯康首席研究员”。主要研究方向为有限元方法和电磁场、磁流体计算。