SIAM Journal on Control and Optimization
Adaptive Lagrange — Galerkin methods for unsteady convection-diffusion problems
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
SIAM Journal on Control and Optimization
A Posteriori Error Estimates for Control Problems Governed by Stokes Equations
SIAM Journal on Numerical Analysis
Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
SIAM Journal on Control and Optimization
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
Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)
Journal of Computational and Applied Mathematics
A posteriori error estimates for optimal distributed control governed by the evolution equations
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
Hi-index | 0.00 |
In this paper, we investigate a characteristic finite element approximation of quadratic optimal control problems governed by linear advection-dominated diffusion equations, where the state and co-state variables are discretized by piecewise linear continuous functions and the control variable is approximated by piecewise constant functions. We derive some a priori error estimates for both the control and state approximations. It is proved that these approximations have convergence order $\mathcal{O}(h_{U}+h+k)$ , where h U and h are the spatial mesh-sizes for the control and state discretization, respectively, and k is the time increment. Numerical experiments are presented, which verify the theoretical results.