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Rayleigh‐Ritz and Galerkin finite elements for diffusion‐convection problems
Author(s) -
Smith I. M.,
Farraday R. V.,
O'Connor B. A.
Publication year - 1973
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr009i003p00593
Subject(s) - finite element method , galerkin method , rayleigh–ritz method , mathematics , discontinuous galerkin method , partial differential equation , stability (learning theory) , mathematical analysis , diffusion , extended finite element method , mixed finite element method , finite difference , boundary value problem , computer science , physics , engineering , structural engineering , machine learning , thermodynamics
Finite element methods are presented for the solution of certain two‐dimensional partial differential equations of interest in water resource problems. Earlier work using Galerkin's method for one‐dimensional problems is shown to be a prototype finite element technique. It is suggested that previous variational (Rayleigh‐Ritz) formulations of finite elements for some problems are misleading and are of limited application when compared with Galerkin's method. The accuracy and stability of the techniques presented are discussed in relation to the well‐known ‘numerical diffusion and dispersion’ phenomena prevalent in popular finite difference methods.