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Finite element methods for second order differential equations with significant first derivatives
Author(s) -
Christie I.,
Griffiths D. F.,
Mitchell A. R.,
Zienkiewicz O. C.
Publication year - 1976
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.1620100617
Subject(s) - mathematics , basis function , finite element method , galerkin method , quadratic equation , basis (linear algebra) , mathematical analysis , boundary value problem , geometry , physics , thermodynamics
Abstract Galerkin finite element methods based on symmetric pyramid basis functions give poor accuracy when applied to second order elliptic equations with large coefficients of the first order terms. This is particularly so when the mesh size is such that oscillations are present in the numerical solution. In the present note asymmetric linear and quadratic basis functions are introduced and shown to overcome this difficulty in an appropriate two point boundary value problem. In particular symmetric quadratic basis functions are oscillation free and highly accurate for a working range of mesh sizes.