We derive and analyze adaptive solvers for boundary value problems in which the differential operator depends affinely on a sequence of parameters. These methods converge uniformly in the parameters and provide an upper bound for the maximal error. Numerical computations indicate that they are more efficient than similar methods that control the error in a mean square sense.
Mots-clés : parametric partial differential equations, partial differential equations with random coefficients, uniform convergence, adaptive methods, operator equations
@article{M2AN_2012__46_6_1485_0,
author = {Gittelson, Claude Jeffrey},
title = {Uniformly convergent adaptive methods for a class of parametric operator equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1485--1508},
publisher = {EDP-Sciences},
volume = {46},
number = {6},
year = {2012},
doi = {10.1051/m2an/2012013},
mrnumber = {2996337},
zbl = {1276.65068},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2012013/}
}
TY - JOUR AU - Gittelson, Claude Jeffrey TI - Uniformly convergent adaptive methods for a class of parametric operator equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 1485 EP - 1508 VL - 46 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2012013/ DO - 10.1051/m2an/2012013 LA - en ID - M2AN_2012__46_6_1485_0 ER -
%0 Journal Article %A Gittelson, Claude Jeffrey %T Uniformly convergent adaptive methods for a class of parametric operator equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1485-1508 %V 46 %N 6 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2012013/ %R 10.1051/m2an/2012013 %G en %F M2AN_2012__46_6_1485_0
Gittelson, Claude Jeffrey. Uniformly convergent adaptive methods for a class of parametric operator equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 1485-1508. doi : 10.1051/m2an/2012013. http://archive.numdam.org/articles/10.1051/m2an/2012013/
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