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Mathematics of Computation

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Numerical approximations to nonlinear conservation laws with locally varying time and space grids


Authors: Stanley Osher and Richard Sanders
Journal: Math. Comp. 41 (1983), 321-336
MSC: Primary 65M10; Secondary 65M05, 76-08
DOI: https://doi.org/10.1090/S0025-5718-1983-0717689-8
MathSciNet review: 717689
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Abstract: An explicit time differencing technique is introduced to approximate nonlinear conservation laws. This differencing technique links together an arbitrary number of space regimes containing fine and coarse time increments. Previous stability requirements, i.e. the CFL condition, placed a global bound on the size of the time increments. For scalar, monotone, approximations in one space dimension, using this variable step time differencing, convergence to the correct physical solution is proven given only a local CFL condition.


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DOI: https://doi.org/10.1090/S0025-5718-1983-0717689-8
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society