✦ LIBER ✦

Finite element methods for second order differential equations with significant first derivatives

✍ Scribed by I. Christie; D. F. Griffiths; A. R. Mitchell; O. C. Zienkiewicz

Publisher: John Wiley and Sons
Year: 1976
Tongue: English
Weight: 316 KB
Volume: 10
Category: Article
ISSN: 0029-5981
DOI: 10.1002/nme.1620100617

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✦ Synopsis

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.

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