Geodesic
A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1557-1581

Voir la notice de l'article provenant de la source Numdam

In this article we develop a posteriori error estimates for second order linear elliptic problems with point sources in two- and three-dimensional domains. We prove a global upper bound and a local lower bound for the error measured in a weighted Sobolev space. The weight considered is a (positive) power of the distance to the support of the Dirac delta source term, and belongs to the Muckenhoupt's class A2. The theory hinges on local approximation properties of either Clément or Scott-Zhang interpolation operators, without need of modifications, and makes use of weighted estimates for fractional integrals and maximal functions. Numerical experiments with an adaptive algorithm yield optimal meshes and very good effectivity indices.

DOI : 10.1051/m2an/2014010
Classification : 35J15, 65N12, 65N15, 65N30, 65N50, 65Y20
Keywords: elliptic problems, point sources, a posteriori error estimates, finite elements, weighted Sobolev spaces 
@article{M2AN_2014__48_6_1557_0,
     author = {Agnelli, Juan Pablo and Garau, Eduardo M. and Morin, Pedro},
     title = {\protect\emph{A posteriori }error estimates for elliptic problems with {Dirac} measure terms in weighted spaces},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1557--1581},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {6},
     year = {2014},
     doi = {10.1051/m2an/2014010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2014010/}
}
TY  - JOUR
AU  - Agnelli, Juan Pablo
AU  - Garau, Eduardo M.
AU  - Morin, Pedro
TI  - A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2014
SP  - 1557
EP  - 1581
VL  - 48
IS  - 6
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2014010/
DO  - 10.1051/m2an/2014010
LA  - en
ID  - M2AN_2014__48_6_1557_0
ER  - 
%0 Journal Article
%A Agnelli, Juan Pablo
%A Garau, Eduardo M.
%A Morin, Pedro
%T A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2014
%P 1557-1581
%V 48
%N 6
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2014010/
%R 10.1051/m2an/2014010
%G en
%F M2AN_2014__48_6_1557_0
Agnelli, Juan Pablo; Garau, Eduardo M.; Morin, Pedro. A posteriori error estimates for elliptic problems with Dirac measure terms in weighted spaces. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1557-1581. doi: 10.1051/m2an/2014010

Cité par Sources :