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DOI: 10.23952/jnfa.2024.12
Received December 18, 2023; Accepted June 3, 2024; Published June 21, 2024
Abstract. This paper presents an interpolated coefficient characteristic mixed finite element method for semilinear convection-diffusion optimal control problems. The hyperbolic parts of the state or co-state equations are combined to form a material derivative, which is then discretized by backward difference. The diffusion terms are discretized by the lowest order Raviart-Thomas mixed finite elements, and the nonlinear terms are treated with interpolated coefficient technique. The numerical solution of the control variable is obtained by the variational discretization. Optimal a priori error estimates are derived for the control, state and co-state. Numerical examples are provided to confirm the theoretical results.
How to Cite this Article:
Y. Hua, Y. Tang, Z. Chen, Interpolated coefficient characteristic mixed finite element method for semilinear convection-diffusion optimal control problems, J. Nonlinear Funct. Anal. 2024 (2024) 12.