TITLE

Superconvergence analysis of fully discrete finite element methods for semilinear parabolic optimal control problems

AUTHOR(S)
Tang, Yuelong; Chen, Yanping
PUB. DATE
April 2013
SOURCE
Frontiers of Mathematics in China;Apr2013, Vol. 8 Issue 2, p443
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We study the superconvergence property of fully discrete finite element approximation for quadratic optimal control problems governed by semilinear parabolic equations with control constraints. The time discretization is based on difference methods, whereas the space discretization is done using finite element methods. The state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions. First, we define a fully discrete finite element approximation scheme for the semilinear parabolic control problem. Second, we derive the superconvergence properties for the control, the state and the adjoint state. Finally, we do some numerical experiments for illustrating our theoretical results.
ACCESSION #
86406846

 

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