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On finite element methods for convection dominated phenomena
Author(s) -
Kikuchi Fumio,
Ushijima Teruo,
Fujita H.
Publication year - 1982
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670040108
Subject(s) - mathematics , finite element method , mathematical analysis , mixed finite element method , piecewise , piecewise linear function , variable (mathematics) , extended finite element method , boundary value problem , backward euler method , convergence (economics) , euler equations , physics , economics , thermodynamics , economic growth
The aim of this work is to give theoretical justification of several types of finite element approximations to the initial‐boundary value problems of first order linear hyperbolic equations. Our approximate scheme is obtained by the piecewise linear continuous finite element method for space variable, x , and the Euler type step by step integration method for time variable, t . An artificial viscosity technique, up‐stream type methods are considered within the frame work of L 2 ‐theory. The convergence and the error estimate of the approximate solutions to the true one are discussed.