Error Estimates and Superconvergence of RT0 Mixed Methods for a Class of Semilinear Elliptic Optimal Control Problems
Year: 2013
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 4 : pp. 637–656
Abstract
In this paper, we will investigate the error estimates and the superconvergence property of mixed finite element methods for a semilinear elliptic control problem with an integral constraint on control. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element and the control variable is approximated by piecewise constant functions. We derive some superconvergence properties for the control variable and the state variables. Moreover, we derive $L^∞$- and $H^{-1}$-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2013.1230nm
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 4 : pp. 637–656
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Semilinear elliptic equations optimal control problems superconvergence error estimates mixed finite element methods.
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