Abstract
Front tracking in combination with dimensional splitting is analyzed as a numerical method for scalar conservation laws in two space dimensions. An analytic error bound is derived, and convergence rates based on numerical experiments are presented. Numerical experiments indicate that large CFL numbers can be usedwithoutlossofaccuracyforawiderangeofproblems. Anewmethodforgridrefinementisintroduced. The method easily allows for dynamical changes in the grid, using, for instance, the total variation in each gridcellasacriterionforintroducingneworremovingexistingrefinements. Severalnumericalexamplesare included, highlighting the features of the numerical method. A comparison with a high-resolution method confirms that dimensional splitting with front tracking is a highly viable numerical method for practical computations. c 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 627{648, 1998
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