TY - JOUR
T1 - A Posteriori Error Estimates for Discontinuous Galerkin Time-Stepping Method for Optimal Control Problems Governed by Parabolic Equations
AU - Liu, Wenbin
AU - Ma, Heping
AU - Tang, Tao
AU - Yan, Ningning
N1 - Funding information:
This work was supported in part by Hong Kong Baptist University, Hong Kong Research Grants Council, and the British EPSRC GR/S11329.
Department of Mathematics, Shanghai University, Shanghai 200436, China ([email protected]. cn). This author’s research was also supported by the Special Funds for State Major Basic Research Projects of China G1999032804 and the Special Funds for Major Specialities of Shanghai Education Committee.
Institute of System Sciences, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China ([email protected]). This author’s research was also supported by the Special Funds for Major State Basic Research Projects (G2000067102), National Natural Science Foundation of China (19931030), and Innovation Funds of the Academy of Mathematics and System Sciences, CAS.
Publisher copyright:
Copyright © 2004 Society for Industrial and Applied Mathematics
PY - 2004/7/29
Y1 - 2004/7/29
N2 - In this paper, we examine the discontinuous Galerkin (DG) finite element approximation to convex distributed optimal control problems governed by linear parabolic equations, where the discontinuous finite element method is used for the time discretization and the conforming finite element method is used for the space discretization. We derive a posteriori error estimates for both the state and the control approximation, assuming only that the underlying mesh in space is nondegenerate. For problems with control constraints of obstacle type, which are the kind most frequently met in applications, further improved error estimates are obtained.
AB - In this paper, we examine the discontinuous Galerkin (DG) finite element approximation to convex distributed optimal control problems governed by linear parabolic equations, where the discontinuous finite element method is used for the time discretization and the conforming finite element method is used for the space discretization. We derive a posteriori error estimates for both the state and the control approximation, assuming only that the underlying mesh in space is nondegenerate. For problems with control constraints of obstacle type, which are the kind most frequently met in applications, further improved error estimates are obtained.
KW - A posteriori error analysis
KW - Discontinuous galerkin method
KW - Finite element approximation
KW - Optimal control
UR - http://www.scopus.com/inward/record.url?scp=21244485903&partnerID=8YFLogxK
U2 - 10.1137/S0036142902397090
DO - 10.1137/S0036142902397090
M3 - Journal article
AN - SCOPUS:21244485903
SN - 0036-1429
VL - 42
SP - 1032
EP - 1061
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 3
ER -