A priori and a posteriori error estimates of H1-Galerkin mixed finite element methods for optimal control problems governed by pseudo-hyperbolic integro-differential equations

Hongbo Chen and Tianliang Hou

Applied Mathematics and Computation, 2018, vol. 328, issue C, 100-112

Abstract: In this paper, we investigate a priori and a posteriori error estimates of H1-Galerkin mixed finite element methods for optimal control problems governed by pseudo-hyperbolic 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. Based on two new elliptic projections, we derive a priori error estimates both for the control variable, the state variable and the co-state variable. The related a priori error estimates for the new projections error are also established. Moreover, a posteriori error estimates for all variables are derived via energy method. Such a posteriori error estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

Keywords: Pseudo-hyperbolic integro-differential equations; Optimal control problems; A priori error estimates; A posteriori error estimates; H1-Galerkin mixed finite element methods (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:328:y:2018:i:c:p:100-112

DOI: 10.1016/j.amc.2018.01.042

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