L∞-error estimates for mixed methods for elliptic partial differential equations
SIAM Journal on Numerical Analysis
SIAM Journal on Control and Optimization
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
Finite Elements in Analysis and Design
A posteriori error estimates for mixed finite element solutions of convex optimal control problems
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
Adaptive computations on conforming quadtree meshes
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
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In this paper we study the fully discrete mixed finite element methods for quadratic convex optimal control problem governed by parabolic equations. 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 is approximated by piecewise constant functions. By applying some error estimates techniques of standard mixed finite element methods, we derive a priori error estimates both for the coupled state and the control approximation. Finally, we present some numerical examples which confirm our theoretical results.