On convergence of monotone finite difference schemes with variable spatial differencing

Author:
Richard Sanders

Journal:
Math. Comp. **40** (1983), 91-106

MSC:
Primary 65M05; Secondary 65M10, 65M15

DOI:
https://doi.org/10.1090/S0025-5718-1983-0679435-6

MathSciNet review:
679435

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Abstract: Monotone finite difference schemes used to approximate solutions of scalar conservation laws have the advantage that these approximations can be proved to converge to the proper solution as the mesh size tends to zero. The greatest disadvantage in using such approximating schemes is the computational expense encountered since monotone schemes can have at best first order accuracy. Computation savings and effective accuracy could be gained if the spatial mesh were refined in regions of expected rapid solution variation.

In this paper we prove that standard monotone difference schemes, (satisfying a fairly unrestrictive CFL condition), converge to the "correct" physical solution even in the case when a nonuniform spatial mesh is employed.

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0679435-6

Article copyright:
© Copyright 1983
American Mathematical Society