Analysis and finite element approximations for distributed optimal control problems for implicit parabolic equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:231

Article

Chrysafinos, Konstantinos

关键词: Error estimates;    Finite element methods;    Distributed optimal control;    Implicit parabolic equations;    Convection-diffusion equations;    Lagrangian coordinates;    Moving meshes;   

DOI  :  10.1016/j.cam.2009.02.092

来源: Elsevier

【 摘 要 】

This work concerns analysis and error estimates for optimal control problems related to implicit parabolic equations. The minimization of the tracking functional subject to implicit parabolic equations is examined. Existence of an optimal solution is proved and an optimality system of equations is derived. Semi-discrete (in space) error estimates for the finite element approximations of the optimality system are presented. These estimates are symmetric and applicable for higher-order discretizations. Finally, fully-discrete error estimates of arbitrarily high-order are presented based on a discontinuous Galerkin (in time) and conforming (in space) scheme. Two examples related to the Lagrangian moving mesh Galerkin formulation for the convection-diffusion equation are described. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free