Abstract
In this paper a posteriori error estimate for continuous interior penalty Galerkin approximation of transient convection dominated diffusion optimal control problems with control constraints is presented. The state equation is discretized by the continuous interior penalty Galerkin method with continuous piecewise linear polynomial space and the control variable is approximated by implicit discretization concept. By use of the elliptic reconstruction technique proposed for parabolic equations, a posteriori error estimates for state variable, adjoint state variable and control variable are proved, which can be used to guide the mesh refinement in the adaptive algorithm.
Highlights
Transient convection diffusion optimal control problems are widely used to model some engineering problems, for example, air pollution problem [, ] and waste water treatment [ ]
One approach to improve the quality of a numerical solution is to exploit special mesh which is locally refined near the boundary layers, for example, Shishkin-type mesh or adaptive mesh
As we know the key problem of the adaptive finite element method is the a posteriori error estimate
Summary
Transient convection diffusion optimal control problems are widely used to model some engineering problems, for example, air pollution problem [ , ] and waste water treatment [ ]. In [ ] the authors discuss adaptive characteristic finite element approximation of transient convection diffusion optimal control problems with a general diffusion coefficient, where a posteriori error estimates in L ( , T; L ( )) norm are derived by dual argument skill for the state and adjoint state variables. The primary interest of this paper is to derive a posteriori error estimates for the following transient convection diffusion optimal control problem with dominance convection:
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