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Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations
Authors:Tianliang Hou & Li Li
Abstract:In this paper, we investigate the error estimates of mixed finite elementmethods for optimal control problems governed by general elliptic equations. Thestate and co-state are approximated by the lowest order Raviart-Thomas mixed finiteelement 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 statevariables. Finally, a numerical example is given to demonstrate the theoretical results.
Keywords:General elliptic equations   optimal control problems   superconvergence   error estimates   mixed finite element methods.
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