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

Abstract

MSC: 49J20 65M15 65M25 65M60 Keywords:Characteristic finite element method Optimal control problems Convection-diffusion equations Pointwise inequality constraints A priori error estimates a b s t r a c t In this paper we analyze a characteristic finite element approximation of convex optimal control problems governed by linear convection-dominated diffusion equations with pointwise inequality constraints on the control variable, where the state and co-state variables are discretized by piecewise linear continuous functions and the control variable is approximated by either piecewise constant functions or piecewise linear discontinuous functions. A priori error estimates are derived for the state, co-state and the control. Numerical examples are given to show the efficiency of the characteristic finite element method.

A granular computing method for nonlinear convection-diffusion equation

“…Under assumptions (a-f) and 't is sufficient small. To derive the following main result, some useful lemmas are needed [20] [21]. we have the error estimate:…”

A Characteristic Finite Element Method for Constrained Convection-Diffusion-Reaction Optimal Control Problems

“…To the best of the authors' knowledge, recently there are some growing published results on optimal control problems governed by steady convection-diffusion equations; see [3,4] of SUPG method, [5] of the standard finite element discretizations with stabilization, [6] of symmetric stabilization method, [7] of edge-stabilization method, [8] of the application of RT mixed DG scheme, [9] of domain decomposition method and so on. However, for the approximation of constrained optimal control problems governed by time-dependent convection-diffusion equations, it is much more complicated and only a few paper has been published, see [10][11][12][13] for example. Systematic 89 introductions of the finite element method for PDEs and optimal control problems can be found in, for example, [14][15][16][17].…”

A Mixed Discontinuous Galerkin Approximation of Time Dependent Convection Diffusion Optimal Control Problem

“…The discontinuous Galerkin approximation including primary discontinuous Galerkin method and local discontinuous Galerkin method is addressed in [7][8][9][10][11][12]. In [13] the authors discuss the characteristic finite element approximation of transient convection diffusion optimal control problem. For more references, one can refer to [14].…”