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中国科学院数学与系统科学研究院龚伟研究员学术报告

发布日期:2022-07-07     作者: admin     浏览数:    分享到:

报告题目:Optimal convergence of finite element approximation to an optimization problem with PDE constraint

报告人:龚伟研究员

报告时间:20227710:00-12:00

报告形式:腾讯会议ID 942-955-838

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https://meeting.tencent.com/dm/OgDfCXTB6zfH


报告摘要:In this talk we consider the optimal convergence of finite element approximation to an optimization problem with PDE constraint. Specifically, we consider an elliptic distributed optimal control problem without control constraints, which can also be viewed as a regularized inverse source problem. The main contributions are two-fold. First, we derive a priori and a posteriori error estimates for the optimization problems, under an appropriately chosen norm that allows us to establish an isomorphism between the solution space and its dual. These results yield error estimates with explicit dependence on the regularization parameter so that the constants appeared in the derivation are independent of it. Second, we prove the contraction property and rate optimality for the adaptive algorithm with respect to the error estimator and solution errors between the adaptive finite element solutions and the continuous solutions. Extensive numerical experiments are presented that confirm our theoretical results.

龚伟,中国科学院数学与系统科学研究院,研究员。2009年于中国科学院数学与系统科学研究院获得博士学位。2009年至今在中国科学院数学与系统科学研究院工作,期间于2010年至2012年在德国汉堡大学数学系做洪堡学者。主要研究方向包括有限元方法,偏微分方程约束优化问题的数值方法。龚伟主持完成多项国家自然科学基金青年基金项目;现主持一项国家自然科学基金面上项目。2017年入选中国科学院数学与系统科学研究院陈景润未来之星。


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