Speaker:Gong Wei,Associate Researcher, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Date:Nov.23, 2021

Time:9:30-10:30

Location:Tencent Meeting, ID:913 428 539

Sponsor:School of Mathematics, Shandong University

Abstract:

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.

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https://www.view.sdu.edu.cn/info/1020/159380.htm