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An ADI Petrov–Galerkin method with quadrature for parabolic problems
Author(s) -
Bialecki B.,
Ganesh M.,
Mustapha K.
Publication year - 2009
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20391
Subject(s) - mathematics , petrov–galerkin method , quadrature (astronomy) , mathematical analysis , elliptic operator , boundary value problem , galerkin method , laplace transform , operator (biology) , alternating direction implicit method , convergence (economics) , partial derivative , partial differential equation , finite element method , finite difference method , biochemistry , chemistry , physics , repressor , economic growth , gene , transcription factor , electrical engineering , economics , thermodynamics , engineering
We propose and analyze a fully discrete Laplace modified alternating direction implicit quadrature Petrov–Galerkin (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.© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009