An ADI Petrov-galerkin method with quadrature for parabolic problems

B. Blalecki; M. Ganesh; K. Mustapha

doi:10.1002/num.20391

An ADI Petrov-galerkin method with quadrature for parabolic problems

B. Blalecki^*, M. Ganesh, K. Mustapha

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We propose and analyze a fully discrete Laplace modified alternating direction implicit quadrature PetrovGalerkin (ADI-QPG) method for solving parabolic initial-boundary value problems on rectangular domains. We prove optimal order convergence results for a restricted class of the associated elliptic operator and demonstrate accuracy of our scheme with numerical experiments for some parabolic problems with variable coefficients.

Original language	English
Pages (from-to)	1129-1148
Number of pages	20
Journal	Numerical Methods for Partial Differential Equations
Volume	25
Issue number	5
DOIs	https://doi.org/10.1002/num.20391
State	Published - Sep 2009

Keywords

ADI
Gauss quadrature
Laplace modified
Parabolic initial-boundary value problems
Petrov-galerkin
Splines

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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Cite this

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title = "An ADI Petrov-galerkin method with quadrature for parabolic problems",

abstract = "We propose and analyze a fully discrete Laplace modified alternating direction implicit quadrature PetrovGalerkin (ADI-QPG) method for solving parabolic initial-boundary value problems on rectangular domains. We prove optimal order convergence results for a restricted class of the associated elliptic operator and demonstrate accuracy of our scheme with numerical experiments for some parabolic problems with variable coefficients.",

keywords = "ADI, Gauss quadrature, Laplace modified, Parabolic initial-boundary value problems, Petrov-galerkin, Splines",

author = "B. Blalecki and M. Ganesh and K. Mustapha",

year = "2009",

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doi = "10.1002/num.20391",

language = "English",

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T1 - An ADI Petrov-galerkin method with quadrature for parabolic problems

AU - Blalecki, B.

AU - Ganesh, M.

AU - Mustapha, K.

PY - 2009/9

Y1 - 2009/9

N2 - We propose and analyze a fully discrete Laplace modified alternating direction implicit quadrature PetrovGalerkin (ADI-QPG) method for solving parabolic initial-boundary value problems on rectangular domains. We prove optimal order convergence results for a restricted class of the associated elliptic operator and demonstrate accuracy of our scheme with numerical experiments for some parabolic problems with variable coefficients.

AB - We propose and analyze a fully discrete Laplace modified alternating direction implicit quadrature PetrovGalerkin (ADI-QPG) method for solving parabolic initial-boundary value problems on rectangular domains. We prove optimal order convergence results for a restricted class of the associated elliptic operator and demonstrate accuracy of our scheme with numerical experiments for some parabolic problems with variable coefficients.

KW - ADI

KW - Gauss quadrature

KW - Laplace modified

KW - Parabolic initial-boundary value problems

KW - Petrov-galerkin

KW - Splines

UR - https://www.scopus.com/pages/publications/67849121240

U2 - 10.1002/num.20391

DO - 10.1002/num.20391

M3 - Article

AN - SCOPUS:67849121240

SN - 0749-159X

VL - 25

SP - 1129

EP - 1148

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 5

ER -

An ADI Petrov-galerkin method with quadrature for parabolic problems

Abstract

Keywords

ASJC Scopus subject areas

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