Enriched finite element methods for unsteady reaction-diffusion problems

Communications in Numerical Methods in Engineering

Volumn 22, Issue 6, 2006, Pages 619-625

  Franca, L P ^a   Ramalho, J V A ^b   Valentin, F ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

Author keywords

Multiscale functions; Reaction diffusion; Singularly perturbed equations; Unsteady problems

Indexed keywords

BUBBLES (IN FLUIDS); DIFFUSION; GALERKIN METHODS; PERTURBATION TECHNIQUES; VARIATIONAL TECHNIQUES;

MULTISCALE FUNCTIONS; REACTION-DIFFUSION; SINGULARLY PERTURBED EQUATIONS; UNSTEADY PROBLEMS;

FINITE ELEMENT METHOD;

BUBBLES (IN FLUIDS); DIFFUSION; FINITE ELEMENT METHOD; GALERKIN METHODS; PERTURBATION TECHNIQUES; VARIATIONAL TECHNIQUES;

EID: 33745587535     PISSN: 10698299     EISSN: 10990887     Source Type: Journal    
DOI: 10.1002/cnm.838     Document Type: Article

References (15)

1. Roos HG, Stynes M, Tobiska L. Numerical Methods for Singularly Perturbed Differential Equations: Convection Diffusion and Flow Problems. Springer: Berlin, 1996.
2. Harari I. Stability of semidiscrete formulations for parabolic problems at small time steps. Computer Methods in Applied Mechanics and Engineering 2004; 193:1491-1516.
3. Franca LP, do Carmo EGD. The Galerkin gradient least-squares method. Computer Methods in Applied Mechanics and Engineering 1989; 74:41-54.
4. Franca LP, Valentin F. On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation. Computer Methods in Applied Mechanics and Engineering 2000; 190:1785-1800.
5. Harari I, Hughes TJR. Stabilized finite element methods for steady advection-diffusion with production. Computer Methods in Applied Mechanics and Engineering 1994; 115:165-191.
6. Valentin F, Franca LP. Combining stabilized finite element methods. Computational and Applied Mathematics 1995; 14(3):285-300.
7. Brezzi F, Russo A. Choosing bubbles for advection-diffusion problems. Mathematical Models and Methods in Applied Sciences 1994; 4(4):571-587.
8. Brezzi F, Franca LP, Russo A. Further considerations on residual-free bubbles for advective-diffusive equations. Computer Methods in Applied Mechanics and Engineering 1998; 166:25-33.
9. Franca LP, Madureira AL, Valentin F. Towards multiscale functions: enriching finite element spaces with local but not bubble-like functions. Computer Methods in Applied Mechanics and Engineering 2005; 194:3006-3021.
10. Franca LP, Madureira AL, Tobiska L, Valentin F. Convergence analysis of a multiscale finite element method for singularly perturbed problems. SIAM Multiscale Modeling and Simulation 2005; 4(3):839-866.
11. Hundsdorfer W, Verwer JG. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Springer: Berlin, 2003.
12. Franca LP, Ramalho JVA, Valentin F. Multiscale and residual-free bubble functions for reaction-advection-diffusion problems. International Journal of Multiscale Computer Engineering 2005; 3(3):297-312.
13. Araya R, Valentin F. A multiscale a posteriori error estimate. Computer Methods in Applied Mechanics and Engineering 2005; 194:2077-2094.
14. Ramalho JVA. New enriched finite element methods for unsteady reaction-advection-diffusion models. Ph.D. Thesis, Laboratório Nacional de Computação Científica - LNCC, in preparation.
15. Ilinca F, Hétu J-F. Galerkin gradient least-squares formulation for transient conduction heat transfer. Computer Methods in Applied Mechanics and Engineering 2002; 191:3073-3097.