Decoupled Mixed Element Methods for Fourth Order Elliptic Optimal Control Problems with Control Constraints

Decoupled Mixed Element Methods for Fourth Order Elliptic Optimal Control Problems with Control Constraints

Year:    2020

Author:    Chang Jin, Yue Shen, Chang Jin

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 400–432

Abstract

In this paper, we study the finite element methods for distributed optimal control problems governed by the biharmonic operator. Motivated from reducing the regularity of solution space, we use the decoupled mixed element method which was used to approximate the solution of biharmonic equation to solve the fourth order optimal control problems. Two finite element schemes, i.e., Lagrange conforming element combined with full control discretization and the nonconforming Crouzeix-Raviart element combined with variational control discretization, are used to discretize the decoupled optimal control system. The corresponding a priori error estimates are derived under appropriate norms which are then verified by extensive numerical experiments.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2019-0016

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 2 : pp. 400–432

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    33

Keywords:    Fourth order elliptic equation optimal control problem decoupled mixed element method Lagrange element nonconforming Crouzeix-Raviart element a priori error estimates.

Author Details

Chang Jin

Yue Shen

Chang Jin

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