2015
DOI: 10.1007/978-3-319-24785-4
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Error Estimates for Well-Balanced Schemes on Simple Balance Laws

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Cited by 22 publications
(24 citation statements)
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“…For the system (1.1) a class of approximations of Well-Balanced type to the Cauchy problem was studied in [17,16] and in the papers [3,4,5]. In these last papers, suitable L 1 error estimates are derived by means of stability analysis for hyperbolic systems of conservation laws, obtained through a suitable adaptation of the Bressan-Liu-Yang functional [10,9].…”
Section: Introductionmentioning
confidence: 99%
“…For the system (1.1) a class of approximations of Well-Balanced type to the Cauchy problem was studied in [17,16] and in the papers [3,4,5]. In these last papers, suitable L 1 error estimates are derived by means of stability analysis for hyperbolic systems of conservation laws, obtained through a suitable adaptation of the Bressan-Liu-Yang functional [10,9].…”
Section: Introductionmentioning
confidence: 99%
“…Outline of the paper. In this work, we extend the previous analysis to systems of the form (1)(2). For a given α, we are able to compare an entropy weak solution u to some particular stationary solutions.…”
Section: Introductionmentioning
confidence: 91%
“…Proof. First, let us remark that the stability inequality (16) implies that v is a stationary solution of system (1)(2). Indeed, if we choose u 0 = v, the right-hand side of (16) is null, by the properties of h, see Lemma 2.3.…”
Section: Relative Entropy and Nonlinear Stabilitymentioning
confidence: 99%
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