Affiliation:
1. Department of Mathematics , Indian Institute of Science , Bangalore 560012 , India
Abstract
Abstract
In this article, convergence and quasi-optimal rate of convergence of an adaptive finite element method (in short, AFEM) is shown for a general second-order non-selfadjoint elliptic PDE with convection term
b
∈
[
L
∞
(
Ω
)
]
d
{b\in[L^{\infty}(\Omega)]^{d}}
and using minimal regularity of the dual problem, i.e., the solution of the dual problem has only
H
1
{H^{1}}
-regularity, which extends the result [J. M. Cascon, C. Kreuzer, R. H. Nochetto and K. G. Siebert,
Quasi-optimal convergence rate for an adaptive finite element method,
SIAM J. Numer. Anal. 46 2008, 5, 2524–2550]. The theoretical results are illustrated by numerical experiments.