Asymptotic error expansions for the finite element method for second order elliptic problems in R_N, N>=2, I: Local interior expansions
Journal article, 2010
Our aim here is to give sufficient conditions on the finite element spaces near a point so that the error in the finite element method for the function and its derivatives at the point have exact asymptotic expansions in terms of the mesh parameter h, valid for h sufficiently small. Such expansions are obtained from the so-called asymptotic expansion inequalities valid in RN for N ≥ 2, studies by Schatz in [Math. Comp., 67 (1998), pp. 877-899] and [SIAM J. Numer. Anal., 38 (2000), pp. 1269-1293].
elliptic equations
similarity of subspaces
Richardson extrapolation
scalings
local estimates
finite element method
asymptotic error expansion inequalities
Author
Mohammad Asadzadeh
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Alfred, H. Schatz
Cornell University
Wolfgang Wendland
Universitat Stuttgart
SIAM Journal on Numerical Analysis
0036-1429 (ISSN) 1095-7170 (eISSN)
Vol. 48 5 2000-2017Subject Categories (SSIF 2011)
Computational Mathematics
DOI
10.1137/080742737