New elliptic projections and a priori error estimates of H1-Galerkin mixed finite element methods for optimal control problems governed by parabolic integro-differential equations

Tianliang Hou, Jiaqi Zhang, Yanzhong Li and Yueting Yang

Applied Mathematics and Computation, 2017, vol. 311, issue C, 29-46

Abstract: In this paper, we discuss a priori error estimates of H1-Galerkin mixed finite element methods for optimal control problems governed by parabolic integro-differential equations. The state variables and co-state variables are approximated by the lowest order Raviart–Thomas mixed finite element and linear finite element, and the control variable is approximated by piecewise constant functions. Both semidiscrete and fully discrete schemes are considered. Based on some new elliptic projections, we derive a priori error estimates for the control variable, the state variables and the adjoint state variables. The related a priori error estimates for the new projections error are also established. A numerical example is given to demonstrate the theoretical results.

Keywords: Parabolic integro-differential equations; Optimal control problems; A priori error estimates; Elliptic projections; H1-Galerkin mixed finite element methods (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300317302886
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:311:y:2017:i:c:p:29-46

DOI: 10.1016/j.amc.2017.04.036

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().