WEAK-DUALITY BASED ADAPTIVE FINITE ELEMENT METHODS FOR PDE-CONSTRAINED OPTIMIZATION WITH POINTWISE GRADIENT STATE-CONSTRAINTS

作     者：M. Hintermuer Michael Hinze Ronald H.W. Hoppe 

作者机构：Department of Mathematics Humboldt-University of Berlin Germany Department of Mathematics University of Hamburg Germany Department of Mathematics University of Augsburg Germany and Department of MathematicsUniversity of Houston USA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2012年第30卷第2期

页      面：101-123页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Mathematisches Forschungsinstitut Oberwolfach Direct For Mathematical & Physical Scien Division Of Mathematical Sciences Funding Source: National Science Foundation 

主　　题：Adaptive finite element method A posteriori errors Dualization Low regu-larity Pointwise gradient constraints State constraints Weak solutions. 

摘      要：Adaptive finite element methods for optimization problems for second order linear el- liptic partial differential equations subject to pointwise constraints on the l2-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint qualification such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overcome the lack in constraint qualification on the continuous level, the weak Fenchel dual is utilized. Several numerical tests illustrate the performance of the proposed error *** subject classification： 65N30, 90C46, 65N50, 49K20, 49N15, 65K10.