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Implicit, Time-Dependent Variable Grid Finite Difference Methods for the Approximation of a Linear Waterflood

Jim Douglas, Jr. and Mary Fanett Wheeler
Mathematics of Computation
Vol. 40, No. 161 (Jan., 1983), pp. 107-121
DOI: 10.2307/2007365
Stable URL: http://www.jstor.org/stable/2007365
Page Count: 15
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Implicit, Time-Dependent Variable Grid Finite Difference Methods for the Approximation of a Linear Waterflood
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Abstract

An implicit, time-dependent variable grid finite difference method based on the addition of an artificial diffusivity is introduced and analyzed for approximating the solution of a scalar conservation law in a single space variable. No relation between the grids at successive time steps is required for convergence. Two adaptive grid selection procedures are shown to be covered by the analysis. Analogous results are also established for an implicit upwinding procedure.

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