计算与应用讨论班

报告题目：A posteriori error estimation and adaptivity for the finite element discretization of second-order PDE problems set in unbounded domains

报告人：Theophile Chaumont-Frelet（Junior Researcher，Inria）

时间：2026年04月13日（星期一），下午15:00

地点：海纳苑2幢206

摘要：This talk is dedicated to the discretization of second-order PDE problems set in unbounded domains. The approximation procedure for such problems is typically divided into two steps. First (i), a modeling error is introduced by truncating the domain at a finite distance L from the origin. Then (ii), the remaining bounded domain is meshed and the corresponding finite element space is used in the discretization. Standard a posteriori error estimators for this problem only take into account the error incurred in step (ii), but disregard the modeling error introduced in step (i). 

 I will discuss an alternative viewpoint where the whole domain is discretized by an infinite mesh, on which a finite-dimensional finite element space of degree is constructed. The construction of the finite element space implicitly involves a truncation procedure, so that the situation is formally identical to the standard setting. However, the key insight of this interpretation is that one can construct an error estimator that accounts for all the sources of error induced by the discretization. This estimator can in particular steer adaptive mesh refinement algorithms that automatically adjust the truncation of the domain. I will rigorously show that the proposed estimator is reliable and efficient, and that the corresponding adaptive algorithm converges at optimal rates. 

报告人简介：Dr. T. Chaumont-Frelet did his PhD in France at Inria Bordeaux with Helene Barucq and Christian Gout. After that, he did a postdoc in BCAM in Spain under the supervision of David Pardo. He was the recruited as research scientist in Inria Sophia-Antipolis, before moving to Inria Lille. His research focuses mostly on the finite element discretization of wave propagation problem, with a focus on high-order methods, a priori error analysis and a posteriori estimates.

联系人：李雨文（liyuwen@zju.edu.cn）