A Priori Error Estimates for Optimal Control Problems Governed by Transient Advection-Diffusion Equations

A characteristic finite element method for optimal control problems governed by convection–diffusion equations

“…Second, the error estimates are obtained in the framework of L 2 -error and bilateral pointwise inequality control constraints. The results obtained and the techniques used here are also different from that of [17].…”

“…The goal of the present paper is to apply the methods of characteristics to the quadratic optimal control problems governed by linear convection-dominated diffusion equations, and we obtain a priori error estimates for both the control and state approximations. The present paper extends [17] in two aspects: First, it deals with either piecewise linear elements or piecewise constant elements for the control approximation. Second, the error estimates are obtained in the framework of L 2 -error and bilateral pointwise inequality control constraints.…”

Variational multiscale method for the optimal control problems of convection--diffusion--reaction equations

“…We choose the parameters as ϵ = 10 −6 , α = 0.001, ⃗ b = (1, 0) T , and r = 0 [7]. We let y d = sin(πx 1 ) sin(πx 2 ) and f = 0 .…”

Crank–Nicolson finite element methods using symmetric stabilization with an application to optimal control problems subject to transient advection–diffusion equations

“…The design of numerical methods for the solution of optimization problems subject to transient advectiondiffusion-reaction equations, on the other hand, has received relatively little attention in the literature; we cite the work of Fu and Rui [6], where a characterisitic finite element method of first order is analyzed and implemented. We will here show how the above stabilized Crank-Nicolson method can be applied in a framework similar to the one of [6], leading to optimal estimates for smooth solutions of the control problem independent of the diffusion coefficient, and also for high order discretization methods. Consider the following distributed optimal control problem on the space-time domain Q …”