A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems

A Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control Problems

Year:    2015

East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 1 : pp. 85–108

Abstract

A posteriori error estimates of semidiscrete mixed finite element methods for quadratic optimal control problems involving linear parabolic equations are developed. The state and co-state are discretised by Raviart-Thomas mixed finite element spaces of order $k$, and the control is approximated by piecewise polynomials of order $k$ ($k≥0$). We derive our a posteriori error estimates for the state and the control approximations via a mixed elliptic reconstruction method. These estimates seem to be unavailable elsewhere in the literature, although they represent an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.010314.110115a

East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 1 : pp. 85–108

Published online:    2015-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    A posteriori error estimates optimal control problems parabolic equations elliptic reconstruction semidiscrete mixed finite element methods.