ERROR-ESTIMATES AND ADAPTIVE FINITE-ELEMENTS FOR NONLINEAR DIFFUSION-CONVECTION PROBLEMS

Authors
MEDINA J PICASSO M RAPPAZ J
Citation
J. Medina et al., ERROR-ESTIMATES AND ADAPTIVE FINITE-ELEMENTS FOR NONLINEAR DIFFUSION-CONVECTION PROBLEMS, Mathematical models and methods in applied sciences, 6(5), 1996, pp. 689-712
Citations number
36
Categorie Soggetti
Mathematical Method, Physical Science",Mathematics
Journal title
Mathematical models and methods in applied sciences → ACNP
ISSN journal
02182025
Volume
6
Issue
5
Year of publication
1996
Pages
689 - 712
Database
ISI
SICI code
0218-2025(1996)6:5<689:EAAFFN>2.0.ZU;2-G
Abstract
A priori and a posteriori error estimates are presented for nonlinear diffusion-convection problems when using the classical Streamline Upwi nd Petrov-Galerkin (SUPG) scheme and numerical integration. For this p urpose, an abstract framework is developed. A priori estimates are der ived in the H-1 and L(2) norms and the error is bounded above and belo w by an estimator based on the equation residual. An adaptive algorith m requiring the generation of successive Delaunay triangulations is pr oposed and numerical results confirm the efficiency of our approach.