MIXED VIRTUAL ELEMENT APPROXIMATION OF A FOURTH ORDER OPTIMAL CONTROL PROBLEM

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In this article, we study mixed virtual element methods for a distributed optimal control problem governed by a fourth order partial differential equation. By introducing an auxiliary variable, the fourth order equation can be transformed into systems of second order equations. A mixed virtual element discrete scheme for the optimal control problem is established. Moreover, a priori error estimates for auxiliary, state, adjoint state and control variable in H2 and L2 norms are derived. Finally, the theoretical finding is verified by numerical experiments.

Sobre autores

Minghui Yang

School of Mathematics and Statistics, Shandong Normal University

Email: zhouzhaojie@sdnu.edu.cn
250014, Ji’nan, China

Yue Shen

School of Science, Xi’an University of Architecture and Technology

Email: zhouzhaojie@sdnu.edu.cn
710055, Xi’an, China

Zhaojie Zhou

School of Mathematics and Statistics, Shandong Normal University

Autor responsável pela correspondência
Email: zhouzhaojie@sdnu.edu.cn
250014, Ji’nan, China

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Declaração de direitos autorais © Minghui Yang, Yue Shen, Zhaojie Zhou, 2023