A Priori Error Estimates of Crank–Nicolson Finite Volume Element Method for a Hyperbolic Optimal Control Problem |
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Authors: | Xianbing Luo |
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Institution: | School of Science, Guizhou University, Guiyang, China |
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Abstract: | In this article, a Crank–Nicolson linear finite volume element scheme is developed to solve a hyperbolic optimal control problem. We use the variational discretization technique for the approximation of the control variable. The optimal convergent order O(h2 + k2) is proved for the numerical solution of the control, state and adjoint‐state in a discrete L2‐norm. To derive this result, we also get the error estimate (convergent order O(h2 + k2)) of Crank–Nicolson finite volume element approximation for the second‐order hyperbolic initial boundary value problem. Numerical experiments are presented to verify the theoretical results.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1331–1356, 2016 |
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Keywords: | Crank– Nicolson distributed control finite volume element method hyperbolic optimal control problem variational discretization |
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