Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

Year:    2016

Author:    Tianliang Hou, Li Li

Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 1050–1071

Abstract

In this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive $L^2$ and $H^{-1}$-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2014.m807

Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 : pp. 1050–1071

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    General elliptic equations optimal control problems superconvergence error estimates mixed finite element methods.

Author Details

Tianliang Hou

Li Li