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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Error bounds for Glimm difference approximations for scalar conservation laws

Authors: David Hoff and Joel Smoller
Journal: Trans. Amer. Math. Soc. 289 (1985), 611-642
MSC: Primary 65M15; Secondary 35L65, 76L05
MathSciNet review: 784006
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Abstract: We derive error bounds for the Glimm difference approximation to the solution of a genuinely nonlinear scalar conservation law with BV initial data. We show that the $ {L^1}$ error is bounded by $ O(\Delta {x^{1/6}}\vert\log \Delta x\vert)$ in the general case, and by $ O(\Delta {x^{1/2}}\vert\log \Delta x\vert)$ for a generic class of piecewise constant data.

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Article copyright: © Copyright 1985 American Mathematical Society

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