Extrapolation and a-posteriori error estimators of Petrov-Galerkin methods for non-linear Volterra integro-differential equations

S. H. Zhang; T. Lin; Yanping Lin; M. Rao

Extrapolation and a-posteriori error estimators of Petrov-Galerkin methods for non-linear Volterra integro-differential equations

S. H. Zhang, T. Lin, Yanping Lin, M. Rao

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial-value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of a-posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.

Original language	English
Pages (from-to)	407-422
Number of pages	16
Journal	Journal of Computational Mathematics
Volume	19
Issue number	4
Publication status	Published - 1 Jul 2001
Externally published	Yes

Keywords

A-posteriori error estimators
Asymptotic expansions
Interpolation post-processing
Petrov-Galerkin finite element methods
Volterra integro-differential equations

ASJC Scopus subject areas

General Mathematics
Applied Mathematics
Computational Mathematics

Cite this

@article{98deb42f11f24808941b7806a53757e5,

title = "Extrapolation and a-posteriori error estimators of Petrov-Galerkin methods for non-linear Volterra integro-differential equations",

abstract = "In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial-value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of a-posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.",

keywords = "A-posteriori error estimators, Asymptotic expansions, Interpolation post-processing, Petrov-Galerkin finite element methods, Volterra integro-differential equations",

author = "Zhang, {S. H.} and T. Lin and Yanping Lin and M. Rao",

year = "2001",

month = jul,

day = "1",

language = "English",

volume = "19",

pages = "407--422",

journal = "Journal of Computational Mathematics",

issn = "0254-9409",

publisher = "Inst. of Computational Mathematics and Sc./Eng. Computing",

number = "4",

}

TY - JOUR

T1 - Extrapolation and a-posteriori error estimators of Petrov-Galerkin methods for non-linear Volterra integro-differential equations

AU - Zhang, S. H.

AU - Lin, T.

AU - Lin, Yanping

AU - Rao, M.

PY - 2001/7/1

Y1 - 2001/7/1

N2 - In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial-value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of a-posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.

AB - In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial-value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of a-posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.

KW - A-posteriori error estimators

KW - Asymptotic expansions

KW - Interpolation post-processing

KW - Petrov-Galerkin finite element methods

KW - Volterra integro-differential equations

UR - http://www.scopus.com/inward/record.url?scp=0035391295&partnerID=8YFLogxK

M3 - Journal article

SN - 0254-9409

VL - 19

SP - 407

EP - 422

JO - Journal of Computational Mathematics

JF - Journal of Computational Mathematics

IS - 4

ER -

Extrapolation and a-posteriori error estimators of Petrov-Galerkin methods for non-linear Volterra integro-differential equations

Abstract

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this