Geodesic
Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations
Applications of Mathematics, Tome 45 (2000) no. 4, pp. 241-263

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be used to forma posteriori error estimators for accessing actual errors of the Petrov-Galerkin finite element solutions. Numerical examples are also provided to illustrate the theoretical results obtained in this paper.
DOI : 10.1023/A:1022333811602
Classification : 45L05, 65B05, 65L60, 65N30, 65R20
Keywords: Volterra integro-differential equations; Petrov-Galerkin methods; asymptotic expansions; defect correction; a posteriori error estimators 
@article{10_1023_A_1022333811602,
     author = {Zhang, Shuhua and Lin, Tao and Lin, Yanping and Rao, Ming},
     title = {Defect correction and a posteriori error estimation of {Petrov-Galerkin} methods for nonlinear {Volterra} integro-differential equations},
     journal = {Applications of Mathematics},
     pages = {241--263},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2000},
     doi = {10.1023/A:1022333811602},
     mrnumber = {1763171},
     zbl = {1058.65147},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1023/A:1022333811602/}
}
TY  - JOUR
AU  - Zhang, Shuhua
AU  - Lin, Tao
AU  - Lin, Yanping
AU  - Rao, Ming
TI  - Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations
JO  - Applications of Mathematics
PY  - 2000
SP  - 241
EP  - 263
VL  - 45
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1023/A:1022333811602/
DO  - 10.1023/A:1022333811602
LA  - en
ID  - 10_1023_A_1022333811602
ER  - 
%0 Journal Article
%A Zhang, Shuhua
%A Lin, Tao
%A Lin, Yanping
%A Rao, Ming
%T Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations
%J Applications of Mathematics
%D 2000
%P 241-263
%V 45
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1023/A:1022333811602/
%R 10.1023/A:1022333811602
%G en
%F 10_1023_A_1022333811602
Zhang, Shuhua; Lin, Tao; Lin, Yanping; Rao, Ming. Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations. Applications of Mathematics, Tome 45 (2000) no. 4, pp. 241-263. doi: 10.1023/A:1022333811602

Cité par Sources :