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Convergence and Superconvergence of Fully Discrete Finite Element for Time Fractional Optimal Control Problems
College of Science, Hunan University of Science and Engineering, Yongzhou, China
- 1 College of Science, Hunan University of Science and Engineering, Yongzhou, China
American Journal of Computational Mathematics·Volume 11 (2021)·Pages 53–63·Published 1 March 2021·DOI10.4236/ajcm.2021.111005
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Abstract
In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and L 1 scheme in time. The control is obtained by the variational discretization technique. The main purpose of this work is to derive the convergence and superconvergence. A numerical example is presented to validate our theoretical results.
KeywordsTime Fractional Optimal Control ProblemsFinite ElementConvergence and Superconvergence
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