A Review of Unified A Posteriori Finite Element Error Control

作     者：C.Carstensen M.Eigel R.H.W.Hoppe C.Löbhard 

作者机构：Department of MathematicsHumboldt Universität zu BerlinD-10099 BerlinGermany Department of Computational Science and EngineeringYonsei UniversitySeoul 120-749Korea Department of MathematicsUniversity of HoustonHouston TX 77204-3008USA. Institute of MathematicsUniversity of AugsburgD-86159 AugsburgGermany 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2012年第5卷第4期

页      面：509-558页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the German National Science Foundation DFG within the Research Center MATHEON and,with the first author,by the WCU program through KOSEF(R31-2008-000-10049-0) support by the NSF grants DMS-0707602,DMS-0810176,DMS-0811153,DMS-0914788 the German National Science Foundation within the Priority Programs SPP 1253,SPP 1506 the German Federal Ministry for Education and Research(BMBF)within the projects BMBF-FROPT and BMBF-MeFreSim the European Science Foundation(ESF)within the ESF Program OPTPDE 

主　　题：A posteriori error analysis finite element method nonconforming finite element method mixed finite element method adaptive algorithm Poisson equation Laméequations Stokes equations Maxwell equations unified a posteriori error analysis discontinuous Galerkin residual estimator 

摘      要：This paper aims at a general guideline to obtain a posteriori error estimates for the finite element error control in computational partial differential *** the abstract setting of mixed formulations,a generalised formulation of the corresponding residuals is proposed which then allows for the unified estimation of the respective dual ***,this can be done with an approach which is applicable in the same way to conforming,nonconforming and mixed ***,the unified approach is applied to various model *** particular,we consider the Laplace,Stokes,Navier-Lamé,and the semi-discrete eddy current equations.