Premium
Stability and convergence of the spectral Galerkin method for the Cahn‐Hilliard equation
Author(s) -
He Yinnian,
Liu Yunxian
Publication year - 2008
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.20328
Subject(s) - mathematics , galerkin method , discretization , cahn–hilliard equation , convergence (economics) , partial differential equation , uniqueness , spectral method , mathematical analysis , stability (learning theory) , a priori and a posteriori , first order partial differential equation , parabolic partial differential equation , finite element method , physics , philosophy , epistemology , machine learning , computer science , economics , thermodynamics , economic growth
A spectral Galerkin method in the spatial discretization is analyzed to solve the Cahn‐Hilliard equation. Existence, uniqueness, and stabilities for both the exact solution and the approximate solution are given. Using the theory and technique of a priori estimate for the partial differential equation, we obtained the convergence of the spectral Galerkin method and the error estimate between the approximate solution u N ( t ) and the exact solution u ( t ). © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008