A conservative characteristic finite volume element method for solution of the advection-diffusion equation

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 45-48, 2008, Pages 3862-3869

  Rui, Hongxing ^a  

^a SHANDONG UNIVERSITY   (China)

Author keywords

Advection diffusion; Characteristic method; Conservation; Error analysis; Finite volume element

Indexed keywords

ADVECTION; COMPUTATIONAL FLUID DYNAMICS; LINEAR EQUATIONS; PIECEWISE LINEAR TECHNIQUES; SEMICONDUCTOR DOPING; TURBULENT FLOW; TWO DIMENSIONAL;

ADVECTION-DIFFUSION; ADVECTION-DIFFUSION EQUATION; ADVECTION-DIFFUSION PROBLEMS; CHARACTERISTIC METHOD; CONSERVATION; DISCRETIZATION; ERROR ANALYSIS; FINITE VOLUME ELEMENT; FINITE VOLUME ELEMENT METHOD; LAGRANGIAN; PIECE-WISE LINEAR; TIME CONTROL;

FINITE VOLUME METHOD;

EID: 50049104722     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.03.013     Document Type: Article

References (24)

1. Bank R.E., and Rose D.J. Some error estimates for the box method. SIAM J. Numer. Anal. 24 (1987) 777-787
2. Bining P., and Celia M.A. A finite volume Eulerian-Lagrangian localized adjoint method for solution of the contaminant transport equations in two-dimensional multiphase flow systems. Water Resour. Res. 32 (1996) 103-114
3. Cai Z. On the finite volume element method. Numer. Math. 58 (1991) 713-735
4. Celia M.A., Russell T.F., Herrera I., and Ewing R.E. An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation. Adv. Water Resour. 13 (1990) 187-206
5. Celia M.A., and Zisman S. An Eulerian-Lagrangian localized adjoint method for reactive transport in groundwater. In: Gambolati, et al. (Ed). Computational Methods in Water Resources VIII (1990), Springer 383-392
6. Ciarlet P.G. The Finite Element Method for Elliptic Problem (1978), North-Holland Publisher, Amsterdam
7. Douglas Jr. J., and Russell T.F. Numerical methods for convection-dominated diffusion problems based on combining the method of characteristic with finite element or finite difference procedures. SIAM J. Numer. Anal. 19 (1982) 871-885
8. Ewing R.E., Russell T.F., and Wheeler M.F. Simulation of miscible displacement using mixed method and a modified method of characteristic. SPE 12241 (1983) 71-81
9. Ewing R.E., and Wang H. Eulerian-Lagrangian localized adjoint method for convection-diffusion equations and their convergence analysis. IMA J. Numer. Anal. 15 (1995) 405-459
10. Ewing R.E., and Wang H. An optimal-order error estimate to Eulerian-Lagrangian localized adjoint method for variable-coefficient advection-reaction problems. SIAM J. Numer. Anal. 33 (1996) 318-348
11. Healy W., and Russell T.F. Efficient implementation of the modified method of characteristics in finite difference models of solute transport. In: Lehr J. (Ed). Proceeding of Conference in Solving Ground Water Problems with Models (1989), National Well Water Association, Indianapolis, Indiana 483-491
12. Healy W., and Russell T.F. A finite-volume Eulerian-Lagrangian localized adjoint method for the advection-dispersion equation. Water Resour. Res. 29 (1993) 2399-2413
13. Healy W., and Russell T.F. Solution of the advection-dispersion equation in two dimensional by a finite-volume Eulerian-Lagrangian localized adjoint method. Adv. Water Resour. 21 (1998) 11-26
14. Herrera I., Ewing R.E., Celia M.A., and Russell T.F. Eulerian-Lagrangian localized adjoint method: the theoretical framework. Numer. Methods PDEs 9 (1993) 431-458
15. Huang J., and Xi S. On the finite volume element method for general self-adjoint elliptic problems. SIAM J. Numer. Anal. 35 (1998) 1762-1774
16. Li R., Chen Z., and Wu W. Generalized Difference Methods for Differential Equations (2000), Marcel Dekker, New York
17. Neuman S.P. An Eulerian-Lagrangian numerical scheme for the dispersion-convection equation using conjugate space-time grids. J. Comput. Phys. 41 (1981) 270-294
18. Pironneau O. On the transport-diffusion algorithm and its application to the Navier-Stokes equations. Numer. Math. 38 (1982) 309-332
19. H. Rui, M. Tabata, A mass-conservative characteristic finite element method of first-order in time increment for convection-diffusion problems, J. Sci. Comput., submitted for publication.
20. Rui H., and Tabata M. A second order characteristic finite element scheme for convection diffusion problems. Numer. Math. 92 (2002) 161-177
21. Russell T.F. Time stepping along characteristics with incomplete iteration for a Galerkin approximate of miscible displacement in porous media. SIAM J. Numer. Anal. 22 (1985) 970-1013
22. Russell T.F. Eulerian-Lagrangian localized adjoint method for advection-dominated problems. In: Griffiths, and Watson (Eds). Proceeding of the 13th Dundee Conference on Numerical Analysis. Pitman Reserach Notes in Mathematics Series vol. 228 (1990), Longman Scientific and Technical, Harlow, UK 206-228
23. Russell T.F., and Trujillo R.V. Eulerian-Lagrangian localized adjoint methods with variable coefficients in multiple dimension. In: Gambolati, et al. (Ed). Computational Methods in Surface Hydrology (1990), Springer-Verlag, Berlin 357-363
24. Wang H., Dahle H.D., Ewing R.E., Espedal M.S., Sharpley R.C., and Man S. An ELLAM scheme for advection-diffusion equations in two dimension. SIAM J. Sci. Comput. 20 (1999) 2160-2194