A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations
Year: 2011
Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 4 : pp. 439–458
Abstract
In this paper, we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates for both the state and the control approximation. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2011.m1017
Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 4 : pp. 439–458
Published online: 2011-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: A posteriori error estimates quadratic optimal control problems parabolic equations mixed finite element methods.
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