Abstract
The object of this paper is to define a finite difference analogue of a locally conservative Eulerian—Lagrangian method based on mixed finite elements and to prove its convergence. The method is appropriate for convection-dominated diffusive processes; here, it will be considered in the case of a semilinear parabolic equation in a single space variable.
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REFERENCES
T. Arbogast, A. Chilikapati, and M. F. Wheeler, A characteristics-mixed finite element for contaminant transport and miscible displacement, in Computational Methods in Water Resources IX, Vol. 1: Numerical Methods in Water Resources, T. F. Russell et al., eds., Elsevier Applied Science, London, New York, 1992, pp. 77-84.
T. Arbogast and M. F. Wheeler, A characteristics-mixed finite element for advection-dominated transport problems, SIAM J. Numer. Anal., 32 (1995), pp. 404-424.
J. Douglas, Jr., F. Pereira, and L. M. Yeh, A locally conservative Eulerian-Lagrangian numerical method and its application to nonlinear transport in porous media, Computational Geosciences, 4 (2000), pp. 1-40.
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Douglas, J., Huang, CS. A Locally Conservative Eulerian-Lagrangian Finite Difference Method for a Parabolic Equation. BIT Numerical Mathematics 41, 480–489 (2001). https://doi.org/10.1023/A:1021963011595
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DOI: https://doi.org/10.1023/A:1021963011595