A posteriori error estimates for continuous interior penalty Galerkin approximation of transient convection diffusion optimal control problems

Boundary value problems

Hongfei Fu¹  Zhaojie Zhou² 

[1] Department of Computational and Applied Mathematics, China University of Petroleum, Qingdao, China;School of Mathematical Sciences, Shandong Normal University, Jinan, China

关键词: transient convection diffusion optimal control problem;    continuous interior penalty Galerkin method;    elliptic reconstruction;    a posteriori error estimate;   

DOI  :  10.1186/s13661-014-0207-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY