Superconvergence and $L^∞$-Error Estimates of the Lowest Order Mixed Methods for Distributed Optimal Control Problems Governed by Semilinear Elliptic Equations
Year: 2013
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 3 : pp. 479–498
Abstract
In this paper, we investigate the superconvergence property and the $L^∞$-error estimates of mixed finite element methods for a semilinear elliptic control problem. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive some superconvergence results for the control variable. Moreover, we derive $L^∞$-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.2013.1133nm
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 3 : pp. 479–498
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Semilinear elliptic equations distributed optimal control problems superconvergence $L^∞$-error estimates mixed finite element methods.
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A two-grid $ P_0^2 $-$ P_1 $ mixed finite element scheme for semilinear elliptic optimal control problems
Xu, Changling
Chen, Hongbo
AIMS Mathematics, Vol. 7 (2022), Iss. 4 P.6153
https://doi.org/10.3934/math.2022342 [Citations: 3]