Superconvergence of fully discrete rectangular mixed finite element methods of parabolic control problems

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摘要

In this paper, we investigate the superconvergence property of the numerical solution of a quadratic parabolic optimal control problem by using fully discrete mixed finite element methods. The space discretization of the state variable is done using usual mixed finite elements, whereas the time discretization is based on difference methods. The state and the 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 the superconvergence results for the control and the state approximation. Some numerical examples are presented to confirm the theoretical investigations.

论文关键词:49N10,49M15,65M25,65M60,Parabolic equations,Optimal control problems,Superconvergence,Fully discrete mixed finite element methods,Postprocessing

论文评审过程:Received 5 January 2011, Revised 24 June 2013, Available online 23 January 2015.

论文官网地址:https://doi.org/10.1016/j.cam.2014.11.052