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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2007365
Page Count: 15
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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.
Mathematics of Computation © 1983 American Mathematical Society