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Convergence analysis of the streamline diffusion and discontinuous Galerkin methods for the Vlasov‐Fokker‐Planck system
Author(s) -
Asadzadeh M.,
Kowalczyk P.
Publication year - 2005
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.20044
Subject(s) - discretization , mathematics , convergence (economics) , fokker–planck equation , discontinuous galerkin method , partial differential equation , diffusion , galerkin method , stability (learning theory) , mathematical analysis , finite element method , physics , computer science , machine learning , economics , thermodynamics , economic growth
Abstract We prove stability estimates and derive optimal convergence rates for the streamline diffusion and discontinuous Galerkin finite element methods for discretization of the multi‐dimensional Vlasov‐Fokker‐Planck system. The focus is on the theoretical aspects, where we deal with construction and convergence analysis of the discretization schemes. Some related special cases are implemented in M. Asadzadeh [Appl Comput Meth 1(2) (2002), 158–175] and M. Asadzadeh and A. Sopasakis [Comput Meth Appl Mech Eng 191(41–42) (2002), 4641–4661]. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005