Seminars on Numerical Algorithms, Analyses, and Applications：A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation

：董兆楠（法国国家数字科学与技术研究院）
：2026-04-20 10:30
：海韵园行政楼C503

报告人：董兆楠（法国国家数字科学与技术研究院）

时  间：2026年4月20日10:30

地  点：海韵园行政楼C503

内容摘要:

We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and continuous piecewise polynomials in time with an upwind discontinuous Galerkin-type approximation for the second temporal derivative. The proposed scheme accepts dynamic mesh modification, as required by space-time adaptive algorithms, resulting in a discontinuous temporal discretisation when mesh changes occur. We prove \emph{a posteriori} error bounds in the L∞(L2)-norm, using carefully designed temporal and spatial reconstructions; explicit control on the constants (including the spatial and temporal orders of the method) in those error bounds is shown. The convergence behaviour of an error estimator is verified numerically, also taking into account the effect of the mesh change. A space-time adaptive algorithm is proposed and tested numerically.

个人简介：

董兆楠, 法国国家信息与自动化研究所（INRIA，Paris）研究员(Tenured Researcher), 主要研究方向包括：continuous and discontinuous FEM, hp-version FEM, adaptive algorithms, a posteriori error analysis, multiscale methods, polygonal discretization methods, hybrid high-order methods, solver design. 2016年10月在英国University of Leicester师从于间断有限元有限元方法（dG）的专家Emmanuil Georgoulis教授和 Andrea Cangiani教授，获得应用数学博士。 随后在英国University of Leicester从事博士后研究。 2019年在希腊国立数学研究院(IACM-FORTH)做访问学者。2019年11月-2020年9月在英国Cardiff University 数学系做讲师。2020起在法国INRIA研究所开始做研究员。近年来在 SIAM Journal of Numerical Analysis, Mathematics of Computation, SIAM Journal on Scientific Computing等杂志上发表30余篇文章，并在Springer 出版社出版一部专著。

 

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