A method of fractional steps for scalar conservation laws without the CFL condition

Authors:
Helge Holden and Nils Henrik Risebro

Journal:
Math. Comp. **60** (1993), 221-232

MSC:
Primary 65M12; Secondary 35L65

DOI:
https://doi.org/10.1090/S0025-5718-1993-1153165-5

MathSciNet review:
1153165

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Abstract | References | Similar Articles | Additional Information

Abstract: We present a numerical method for the *n*-dimensional initial value problem for the scalar conservation law . Our method is based on the use of dimensional splitting and Dafermos's method to solve the one-dimensional equations. This method is unconditionally stable in the sense that the time step is not limited by the space discretization. Furthermore, we show that this method produces a subsequence which converges to the weak entropy solution as both the time and space discretization go to zero. Finally, two numerical examples are discussed.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1993-1153165-5

Keywords:
Dimensional splitting,
scalar conservation law,
fractional steps,
numerical methods

Article copyright:
© Copyright 1993
American Mathematical Society