Error bounds for a deterministic version of the Glimm scheme

Alberto Bressan; Andrea Marson

doi:10.1007/s002050050088

Error bounds for a deterministic version of the Glimm scheme

Alberto Bressan, Andrea Marson

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

Consider the hyperbolic system of conservation laws u_t + F(u)_x = 0. Let u be the unique viscosity solution with initial condition u(0, x) = ū(x), and let u^ε be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes Δx, Δt = O(Δx). With a suitable choice of the sampling sequence, we prove the estimate ∥u^ε(t, ·) - u(t, ·)∥_L = o(1) · √Δx|ln(Δx)|.

Original language	English (US)
Pages (from-to)	155-176
Number of pages	22
Journal	Archive for Rational Mechanics and Analysis
Volume	142
Issue number	2
DOIs	https://doi.org/10.1007/s002050050088
State	Published - May 28 1998

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s002050050088

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abstract = "Consider the hyperbolic system of conservation laws ut + F(u)x = 0. Let u be the unique viscosity solution with initial condition u(0, x) = ū(x), and let uε be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes Δx, Δt = O(Δx). With a suitable choice of the sampling sequence, we prove the estimate ∥uε(t, ·) - u(t, ·)∥L = o(1) · √Δx|ln(Δx)|.",

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AU - Marson, Andrea

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N2 - Consider the hyperbolic system of conservation laws ut + F(u)x = 0. Let u be the unique viscosity solution with initial condition u(0, x) = ū(x), and let uε be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes Δx, Δt = O(Δx). With a suitable choice of the sampling sequence, we prove the estimate ∥uε(t, ·) - u(t, ·)∥L = o(1) · √Δx|ln(Δx)|.

AB - Consider the hyperbolic system of conservation laws ut + F(u)x = 0. Let u be the unique viscosity solution with initial condition u(0, x) = ū(x), and let uε be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes Δx, Δt = O(Δx). With a suitable choice of the sampling sequence, we prove the estimate ∥uε(t, ·) - u(t, ·)∥L = o(1) · √Δx|ln(Δx)|.

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SN - 0003-9527

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ER -

Error bounds for a deterministic version of the Glimm scheme

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