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Decoupled smooth interfaces for spectral‐element approximations of parabolic or elliptic type
Author(s) -
Black Kelly
Publication year - 1993
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.1690090405
Subject(s) - mathematics , chebyshev filter , smoothing , domain decomposition methods , polynomial , interface (matter) , scheme (mathematics) , derivative (finance) , degree of a polynomial , degree (music) , consistency (knowledge bases) , type (biology) , domain (mathematical analysis) , finite element method , mathematical analysis , geometry , computer science , ecology , statistics , physics , bubble , maximum bubble pressure method , parallel computing , biology , acoustics , financial economics , economics , thermodynamics
A method is examined to approximate the interface conditions for Chebyshev polynomial approximations to the solutions of parabolic problems, and a smoothing technique is used to calculate the interface conditions for a domain decomposition method. The methods uses a polynomial of one less degree then the full approximation to calculate the first derivative so that interface values can be calculated by using only the adjacent subdomains. Theoretical results are given for the consistency of the scheme and practical results are presented. Computational results are given for both a fourth‐order Runga‐Kutta methods and an explicit/implicit scheme. © 1993 John Wiley & Sons, Inc.