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A mass-conservative characteristic finite element scheme for convection-diffusion problems. (English) Zbl 1203.65187
Summary: We develop a mass-conservative characteristic finite element scheme for convection diffusion problems. This scheme preserves the mass balance identity. It is proved that the scheme is essentially unconditionally stable and convergent with first order in time increment and k-th order in element size when the P k element is employed. Some numerical examples are presented to show the efficiency of the present scheme.
MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M25Method of characteristics (IVP of PDE, numerical methods)
76M10Finite element methods (fluid mechanics)
References:
[1]Arbogast, T., Wheeler, M.F.: A characteristics-mixed finite element method for advection-dominated transport problems. SIAM J. Numer. Anal. 32, 404–424 (1995) · Zbl 0823.76044 · doi:10.1137/0732017
[2]Baba, K., Tabata, M.: On a conservative upwind finite element scheme for convective diffusion equations. RAIRO Anal. Numér. (Numer. Anal.) 15, 3–35 (1981)
[3]Boukir, K., Maday, Y., Metivet, B., Razafindrakoto, E.: A high-order characteristics/finite element method for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 25, 1421–1454 (1997) · doi:10.1002/(SICI)1097-0363(19971230)25:12<1421::AID-FLD334>3.0.CO;2-A
[4]Brooks, A.N., Hughes, T.J.R.: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 32, 199–259 (1982) · Zbl 0497.76041 · doi:10.1016/0045-7825(82)90071-8
[5]Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. SIAM, New York (2002)
[6]Douglas, J. Jr., Huang, T.C., Pereira, F.: The modified method of characteristics with adjusted advection. Numer. Math. 83, 353–369 (1999) · Zbl 0936.65115 · doi:10.1007/s002110050453
[7]Douglas, J., Jr., Russell, T.F.: Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. 19, 871–885 (1982) · Zbl 0492.65051 · doi:10.1137/0719063
[8]Ewing, R.E., Wang, H.: An optimal-order estimate for Eulerian-Lagrangian localized adjoint methods for variable-coefficient advection-reaction problems. SIAM J. Numer. Anal. 33, 318–348 (1996) · Zbl 0860.65086 · doi:10.1137/0733017
[9]Glowinski, R.: Numerical Methods for Fluids (Part 3). Handbook of Numerical Analysis, vol. IX, Ciarlet, P.G., Lions, J.L. (eds.). Elsevier, Amsterdam (2003).
[10]Ikeda, T.: Maximum Principle in Finite Element Models for Convection-Diffusion Phenomena. Lecture Notes in Numerical and Applied Analysis, vol. 4. Kinokuniya/North-Holland, Tokyo (1983)
[11]Johnson, C.: Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge Univ. Press, Cambridge (1987)
[12]Kanayama, H.: Discrete models for salinity distribution in a bay: Conservation laws and maximum principle. Theor. Appl. Mech. (Univ. Tokyo Press) 28, 559–579 (1980)
[13]Pironneau, O.: On the transport-diffusion algorithm and its application to the Navier-Stokes equations. Numer. Math. 38, 309–332 (1982) · Zbl 0505.76100 · doi:10.1007/BF01396435
[14]Pironneau, O.: Finite Element Methods for Fluids. Wiley, Chichester (1989)
[15]Rui, H., Tabata, M.: A second order characteristic finite element scheme for convection diffusion problems. Numer. Math. 92, 161–177 (2002) · Zbl 1005.65114 · doi:10.1007/s002110100364
[16]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, 970–1013 (1985) · Zbl 0594.76087 · doi:10.1137/0722059
[17]Tabata, M.: A finite element approximation corresponding to the upwind differencing. Memoirs Numer. Math. 4, 47–63 (1977)
[18]Tabata, M.: L analysis of the finite element method. In: Fujita, H., Yamaguti, M. (eds.) Numerical Analysis of Evolution Equations. Lecture Notes in Numerical and Applied Analysis, vol. 1, pp. 25–62. Kinokuniya, Tokyo (1979)
[19]Tabata, M., Fujima, S.: An upwind finite element scheme for high-Reynolds-number flows. Int. J. Numer. Methods Fluids 12, 305–322 (1991) · Zbl 0715.76012 · doi:10.1002/fld.1650120402
[20]Viozat, C., Held, C., Mer, K., Dervieux, A.: On vertex-centered unstructured finite-volume methods for stretched anisotropic triangulations. Comput. Methods Appl. Mech. Eng. 190, 4733–4766 (2001) · Zbl 0997.76054 · doi:10.1016/S0045-7825(00)00345-5
[21]Wang, H., Dahle, H.K., Ewing, R.E., Espedal, M.S., Sharpley, R.C., Man, S.: An ELLAM scheme for advection-diffusion equations in two dimensions. SIAM J. Sci. Comput. 20, 2160–2194 (1999) · Zbl 0939.65109 · doi:10.1137/S1064827596309396