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 equations.In 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 norms.Notably,this can be done with an approach which is applicable in the same way to conforming,nonconforming and mixed discretisations.Subsequently,the unified approach is applied to various model problems.In particular,we consider the Laplace,Stokes,Navier-Lamé,and the semi-discrete eddy current equations.
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.