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

Jim Douglas, Mary Fanett Wheeler
1983 Mathematics of Computation  
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.
doi:10.2307/2007365 fatcat:fv7fr3ztcngdhhq5humks2cqme