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A Locally Conservative Eulerian-Lagrangian Finite Difference Method for a Parabolic Equation

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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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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

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