TY - JOUR
T1 - Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction
AU - Mingxia Li, Jingzhi Li & Shipeng Mao
JO - Communications in Computational Physics
VL - 4
SP - 1068
EP - 1090
PY - 2014
DA - 2014/04
SN - 15
DO - http://doi.org/10.4208/cicp.050313.210613s
UR - https://global-sci.org/intro/article_detail/cicp/7128.html
KW - 
AB - <p style="text-align: justify;">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.</p>