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http://dx.doi.org/10.4134/BKMS.2013.50.1.321

A POSTERIORI L∞(L2)-ERROR ESTIMATES OF SEMIDISCRETE MIXED FINITE ELEMENT METHODS FOR HYPERBOLIC OPTIMAL CONTROL PROBLEMS  

Hou, Tianliang (Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of Mathematics Xiangtan University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.1, 2013 , pp. 321-341 More about this Journal
Abstract
In this paper, we discuss the a posteriori error estimates of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by linear hyperbolic equations. The state and the co-state are discretized by the order $k$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order $k(k{\geq}0)$. Using mixed elliptic reconstruction method, a posterior $L^{\infty}(L^2)$-error estimates for both the state and the control approximation are derived. Such 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
a posteriori error estimates; optimal control problems; hyperbolic equations; elliptic reconstruction; semidiscrete mixed finite element methods;
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