Flux-stability for conservation laws with discontinuous flux and convergence rates of the front tracking method
| Autor: | Adrian Montgomery Ruf |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Conservation law
Finite volume method Applied Mathematics General Mathematics Numerical analysis Mathematical analysis Scalar (physics) Flux Numerical Analysis (math.NA) 010103 numerical & computational mathematics Classification of discontinuities 01 natural sciences 010101 applied mathematics Computational Mathematics Mathematics - Analysis of PDEs Rate of convergence FOS: Mathematics Piecewise Mathematics - Numerical Analysis 0101 mathematics 35L65 35R05 35B35 65M12 Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | IMA Journal of Numerical Analysis. 42:1116-1142 |
| ISSN: | 1464-3642 0272-4979 |
| DOI: | 10.1093/imanum/draa101 |
| Popis: | We prove that adapted entropy solutions of scalar conservation laws with discontinuous flux are stable with respect to changes in the flux under the assumption that the flux is strictly monotone in u and the spatial dependency is piecewise constant with finitely many discontinuities. We use this stability result to prove a convergence rate for the front tracking method -- a numerical method which is widely used in the field of conservation laws with discontinuous flux. To the best of our knowledge, both of these results are the first of their kind in the literature on conservation laws with discontinuous flux. We also present numerical experiments verifying the convergence rate results and comparing numerical solutions computed with the front tracking method to finite volume approximations. Comment: 22 pages, 10 figures, 2 tables |
| Databáze: | OpenAIRE |
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