THE FINITE-VOLUME ELEMENT METHOD WITH QUADRATIC BASIS FUNCTIONS

Authors
LIEBAU F
Citation
F. Liebau, THE FINITE-VOLUME ELEMENT METHOD WITH QUADRATIC BASIS FUNCTIONS, Computing, 57(4), 1996, pp. 281-299
Citations number
17
Categorie Soggetti
Computer Sciences","Computer Science Theory & Methods
Journal title
Computing → ACNP
ISSN journal
0010485X
Volume
57
Issue
4
Year of publication
1996
Pages
281 - 299
Database
ISI
SICI code
0010-485X(1996)57:4<281:TFEMWQ>2.0.ZU;2-V
Abstract
The paper presents a box scheme with quadratic basis functions for the discretisation of elliptic boundary value problems. The resulting dis cretisation matrix is non-symmetrical (and also not an M-matrix). The stability analysis is based on an elementwise estimation of the scalar product [A(h) u(h), u(h)]. Sufficient conditions placed on the triang les of the triangulation lead to discrete ellipticity. Proof of an O(h (2)) error estimate is given for these conditions.