Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Error Estimates for the Numerical Approximation of a Semilinear Elliptic Control Problem
Computational Optimization and Applications
A posteriori error estimates for control problems governed by nonlinear elliptic equations
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems
SIAM Journal on Numerical Analysis
Superconvergence Properties of Optimal Control Problems
SIAM Journal on Control and Optimization
A posteriori error estimates for mixed finite element solutions of convex optimal control problems
Journal of Computational and Applied Mathematics
A Legendre-Galerkin Spectral Method for Optimal Control Problems Governed by Elliptic Equations
SIAM Journal on Numerical Analysis
A priori error estimates for elliptic optimal control problems with a bilinear state equation
Journal of Computational and Applied Mathematics
Error estimates for parabolic optimal control problem by fully discrete mixed finite element methods
Finite Elements in Analysis and Design
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In this paper, we analyze the superconvergence of the bilinear constrained elliptic optimal control problem by triangular Raviart-Thomas mixed finite element methods. The state and the co-state are approximated by the order k=1 Raviart-Thomas mixed finite elements and the control is approximated by piecewise constant functions. We obtain the superconvergence property between average L^2 projection and the approximation of the control variable, and the convergence order is h^2. Two numerical examples are presented for illustrating the superconvergence results.