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Least‐squares finite elements for first‐order hyperbolic systems
Author(s) -
Carey Graham F.,
Jianng B. N.
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620260106
Subject(s) - finite element method , mathematics , galerkin method , inviscid flow , stability (learning theory) , least squares function approximation , discontinuous galerkin method , extension (predicate logic) , mathematical analysis , petrov–galerkin method , computer science , engineering , structural engineering , mechanics , physics , statistics , machine learning , estimator , programming language
A class of least‐squares finite element methods has been developed for first‐order systems and here we study this approach for hyperbolic problems. The formulation of the least‐squares method is developed in detail and compared with the Petrov‐Galerkin and Taylor‐Galerkin procedures. A stability analysis is carried out and the extension to the non‐linear problem described. Numerical comparison studies demonstrate the performance of the method and suggest that it is a promising alternative to existing schemes. Applications considered include the convection equation, inviscid Burger's equation and shallow‐water equations.