On Convergence of Monotone Finite Difference Schemes with Variable Spatial Differencing
- 1 January 1983
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 40 (161) , 91-106
- https://doi.org/10.2307/2007364
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.Keywords
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