Error bounds for Glimm difference approximations for scalar conservation laws

Hoff, David; Smoller, Joel

doi:10.1090/S0002-9947-1985-0784006-5

Error bounds for Glimm difference approximations for scalar conservation laws
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by David Hoff and Joel Smoller PDF

Trans. Amer. Math. Soc. 289 (1985), 611-642 Request permission

Abstract:

We derive error bounds for the Glimm difference approximation to the solution of a genuinely nonlinear scalar conservation law with $\text {BV}$ initial data. We show that the ${L^1}$ error is bounded by $O(\Delta {x^{1/6}}|\log \Delta x|)$ in the general case, and by $O(\Delta {x^{1/2}}|\log \Delta x|)$ for a generic class of piecewise constant data.

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First order quasilinear equations in several space variables

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