Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction

Li, Mingxia1; Li, Jingzhi2; Mao, Shipeng3

2014-04

10.4208/cicp.050313.210613s

Communications in Computational Physics   影响因子和分区

1815-2406

1991-7120

This paper studies convergence analysis of an adaptive finite element algorithm for numerical estimation of some unknown distributed flux in a stationary heat conduction system, namely recovering the unknown Neumann data on interior inaccessible boundary using Dirichlet measurement data on outer accessible boundary. Besides global upper and lower bounds established in [23], a posteriori local upper bounds and quasi-orthogonality results concerning the discretization errors of the state and adjoint variables are derived. Convergence and quasi-optimality of the proposed adaptive algorithm are rigorously proved. Numerical results are presented to illustrate the quasi-optimality of the proposed adaptive method.

Inverse problems adaptive finite element method a posteriori error estimates quasi-orthogonality convergence analysis

SCI ; CPCI-S

英语

通讯

NSFC[11101386] ; NSFC[11201453] ; NSFC[91130022] ; NSFC[11101414] ; NSFC[91130026]

Physics

Physics, Mathematical

WOS:000340781300012

GLOBAL SCIENCE PRESS

Web of Science

1.China Univ Geosci Beijing, Sch Sci, Beijing 100083, Peoples R China
2.South Univ Sci & Technol China, Fac Sci, Shenzhen 518055, Peoples R China
3.Chinese Acad Sci, AMSS, Inst Computat Math, LSEC, Beijing 100190, Peoples R China

Li, Mingxia,Li, Jingzhi,Mao, Shipeng. Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction[J]. Communications in Computational Physics,2014,15(4):1068-1090.

Li, Mingxia,Li, Jingzhi,&Mao, Shipeng.(2014).Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction.Communications in Computational Physics,15(4),1068-1090.

Li, Mingxia,et al."Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction".Communications in Computational Physics 15.4(2014):1068-1090.