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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- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp. 40 (1983), 107-121
- MSC: Primary 65M10; Secondary 35L65
- DOI: https://doi.org/10.1090/S0025-5718-1983-0679436-8
- MathSciNet review: 679436