An adaptive stabilized finite element scheme for the advection-reaction- diffusion equation

Applied Numerical Mathematics

Volumn 54, Issue 3-4, 2005, Pages 491-503

  Araya, Rodolfo ^a   Behrens, Edwin ^a   Rodríguez, Rodolfo ^a  

^a UNIVERSITY OF CONCEPCIÓN   (Chile)

Author keywords

A posteriori error estimates; Advection reaction diffusion problem; Boundary and inner layers; Stabilized finite elements

Indexed keywords

BOUNDARY CONDITIONS; DIFFUSION; ERRORS; ESTIMATION; GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; LINEAR EQUATIONS; MATHEMATICAL MODELS; OSCILLATIONS; PROBLEM SOLVING; REACTION KINETICS; VECTORS;

A POSTERIORI ERROR ESTIMATES; ADVECTION-REACTION-DIFFUSION PROBLEM; BOUNDARY AND INNER LAYERS; STABILIZED FINITE ELEMENTS;

FINITE ELEMENT METHOD;

EID: 20444473810     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.09.015     Document Type: Conference Paper

References (15)

1. J. Alberty, C. Carstensen, and S.A. Funken Remarks around 50 lines of Matlab: short finite element implementation Numer. Algorithms 20 1999 117 137
2. F. Brezzi, D. Marini, and A. Russo Applications of the pseudo residual-free bubbles to the stabilization of convection-diffusion problems Comput. Methods Appl. Mech. Engrg. 166 1998 51 63
3. A.N. Brooks, and T.J.R. Hughes Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comput. Methods Appl. Mech. Engrg. 32 1982 199 259
4. P. Clément Approximation by finite element functions using local regularization RAIRO R-2 1975 77 84
5. J. Douglas, and J.P. Wang An absolutely stabilized finite element method for the Stokes problem Math. Comp. 52 1989 495 508
6. L.P. Franca, S.L. Frey, and T.J.R. Hughes Stabilized finite element methods. I. Application to the advective-diffusive model Comput. Methods Appl. Mech. Engrg. 95 1992 253 276
7. L.P. Franca, and F. Valentin On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation Comput. Methods Appl. Mech. Engrg. 190 2000 1785 1800
8. T. Knopp, G. Lube, and G. Rapin Stabilized finite element methods with shock capturing for advection-diffusion problems Comput. Methods Appl. Mech. Engrg. 191 2002 2997 3013
9. H.-G. Roos, M. Stynes, and L. Tobiska Numerical Methods for Singularly Perturbed Differential Equations - Convection-Diffusion and Flow Problems Springer Series in Computational Mathematics vol. 24 1996 Springer Berlin
10. G. Sangalli A robust a posteriori estimator for the residual-free bubbles method applied to advection-diffusion problems Numer. Math. 89 2001 379 399
11. J.R. Shewchuk Delaunay refinement algorithms for triangular mesh generation Comput. Geom. Theor. Appl. 22 2002 21 74
12. R. Verfürth Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation Numer. Math. 78 1998 479 493
13. R. Verfürth A posteriori error estimators for convection-diffusion equations Numer. Math. 80 1998 641 663
14. R. Verfürth A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques 1996 Wiley-Teubner Stuttgart
15. S. Wang An a posteriori error estimate for finite element approximations of a singularly perturbed advection-diffusion problem J. Comput. Appl. Math. 87 1997 227 242