New a posteriori error estimates for optimal control problems governed by parabolic integro-differential equations
Hongbo Chen, Tianliang Hou
School of Mathematics and Statistics, Beihua University, Jilin, China
Keywords: parabolic integro-differential equations, finite element, elliptic reconstruction, a posteriori error estimates
Abstract
In this paper, we provide a new a posteriori error analysis for a linear finite element approximation of a parabolic integro-differential optimal control problem. The state and co-state are approximated by piecewise linear functions, while the control variable is discretized by a variational discretization method. We first define elliptic reconstructions of numerical solutions and then discuss a posteriori error estimates for all variables.
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