变分离散与完全离散分裂正定混合有限元相结合的抛物型最优控制问题

IF 1.1 Q1 MATHEMATICS

Journal of Nonlinear Functional Analysis Pub Date : 2023-01-01 DOI:10.23952/jnfa.2023.11

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Variational discretization combined with fully discrete splitting positive definite mixed finite elements for parabolic optimal control problems

. In this paper, we consider a variational discretization combined with fully discrete splitting positive deﬁnite mixed ﬁnite element approximation of parabolic optimal control problems. For the state and co-state, Raviart-Thomas mixed ﬁnite element spaces and backward Euler scheme are used for space and time discretization, respectively. The variational discretization technique is used for the approximation of the control variable. We derive a priori error estimates for the control, state, and co-state. A numerical example is presented to demonstrate the theoretical results.

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来源期刊

Journal of Nonlinear Functional Analysis Multiple-

CiteScore

2.40

自引率

0.00%

发文量

期刊介绍： Journal of Nonlinear Functional Analysis focuses on important developments in nonlinear functional analysis and its applications with a particular emphasis on topics include, but are not limited to: Approximation theory; Asymptotic behavior; Banach space geometric constant and its applications; Complementarity problems; Control theory; Dynamic systems; Fixed point theory and methods of computing fixed points; Fluid dynamics; Functional differential equations; Iteration theory, iterative and composite equations; Mathematical biology and ecology; Miscellaneous applications of nonlinear analysis; Multilinear algebra and tensor computation; Nonlinear eigenvalue problems and nonlinear spectral theory; Nonsmooth analysis, variational analysis, convex analysis and their applications; Numerical analysis; Optimal control; Optimization theory; Ordinary differential equations; Partial differential equations; Positive operator inequality and its applications in operator equation spectrum theory and so forth; Semidefinite programming polynomial optimization; Variational and other types of inequalities involving nonlinear mappings; Variational inequalities.