## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

JIMO

In this paper, we investigate the superconvergence property of a
quadratic elliptic control problem with pointwise control
constraints. The state and the co-state variables are approximated
by the Raviart-Thomas mixed finite element of order
$k=1$ and the control variable is discretized by piecewise linear
but discontinuous functions. Approximations of the optimal solution
of the continuous optimal control problem will be constructed by a
projection of the discrete adjoint state. It is proved that these
approximations have convergence order $h^{2}$.

JIMO

In this paper, a finite element method for a parabolic optimal
control problem is introduced and analyzed. For the discretization
of a quadratic convex optimal control problem, the state and
co-state are approximated by piecewise linear functions and the
control is approximated by piecewise constant functions. As a
result, it is proved in this paper that the difference between a
suitable interpolation of the control and its finite element
approximation has superconvergence property in order $O(h^2)$.
Finally, two numerical examples are presented to confirm our
theoretical results.

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