Convergence and superconvergence of variational discretization for parabolic bilinear optimization problems
Abstract In this paper, we investigate a variational discretization approximation of parabolic bilinear optimal control problems with control constraints. For the state and co-state variables, triangular linear finite element and difference methods are used for space and time discretization, respect...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2195-3 |
| Summary: | Abstract In this paper, we investigate a variational discretization approximation of parabolic bilinear optimal control problems with control constraints. For the state and co-state variables, triangular linear finite element and difference methods are used for space and time discretization, respectively, superconvergence in H1 $H^{1}$-norm between the numerical solutions and elliptic projections are derived. Although the control variable is not discrete directly, convergence of second order in L2 $L^{2}$-norm is obtained. These theoretical results are confirmed by two numerical examples. |
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| ISSN: | 1029-242X |