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Galerkin and collocation‐Galerkin methods with superconvergence and optimal fluxes
Author(s) -
Carey G. F.,
Humphrey D.,
Wheeler M. F.
Publication year - 1981
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.1620170610
Subject(s) - superconvergence , galerkin method , collocation (remote sensing) , orthogonal collocation , mathematics , finite element method , collocation method , numerical analysis , discontinuous galerkin method , gauss , mathematical analysis , computer science , physics , differential equation , thermodynamics , ordinary differential equation , machine learning , quantum mechanics
Abstract Finite element methods are formulated and investigated for the effectiveness factor problem for heat and mass transfer with chemical reactions in catalyst pellet models. A Galerkin finite element method is compared with a previous C 1 collocation method 7 . A scheme that is conceptually intermediate between these two methods and accordingly has been termed collocation‐Galerkin is formulated and numerical experiments considered. Of particular interest here are superconvergence results at the Gauss and Jacobi points, respectively. Numerical studies of superconvergence in the presence of a nonlinear reaction‐rate term are presented. An integral formula is devised and used to compute the flux at the pellet surface to optimal accuracy. Numerical experiments are conducted to demonstrate the improvement in computed fluxes.