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Accuracy of Stable, High-order Finite Difference Methods for Hyperbolic Systems with Non-smooth Wave Speeds
Department of Computer and Information Science 1202, University of Oregon, Eugene, USA / Department of Earth Science 1272 University of Oregon, Eugene, USA.
Southern California Earthquake Center, University of Southern California, Los Angeles, USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2019 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 81, no 3, p. 2356-2387Article in journal (Refereed) Published
Abstract [en]

We derive analytic solutions to the scalar and vector advection equation with variable coefficients in one spatial dimension using Laplace transform methods. These solutions are used to investigate how accuracy and stability are influenced by the presence of discontinuous wave speeds when applying high-order-accurate, skew-symmetric finite difference methods designed for smooth wave speeds. The methods satisfy a summation-by-parts rule with weak enforcement of boundary conditions and formal order of accuracy equal to 2, 3, 4 and 5. We study accuracy, stability and convergence rates for linear wave speeds that are (a) constant, (b) non-constant but smooth, (c) continuous with a discontinuous derivative, and (d) constant with a jump discontinuity. Cases (a) and (b) correspond to smooth wave speeds and yield stable schemes and theoretical convergence rates. Non-smooth wave speeds [cases (c) and (d)], however, reveal reductions in theoretical convergence rates and in the latter case, the presence of an instability.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2019. Vol. 81, no 3, p. 2356-2387
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-161921DOI: 10.1007/s10915-019-01088-wISI: 000495855000003OAI: oai:DiVA.org:liu-161921DiVA, id: diva2:1369867
Available from: 2019-11-13 Created: 2019-11-13 Last updated: 2019-12-09Bibliographically approved

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The full text will be freely available from 2020-11-11 08:00
Available from 2020-11-11 08:00

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Nordström, Jan

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  • apa
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  • de-DE
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