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Spurious solutions for the advection-diffusion equation using wide stencils for approximating the second derivative
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2018 (English)In: Numerical Methods for Partial Differential Equations, ISSN 0749-159X, E-ISSN 1098-2426, Vol. 34, no 2, p. 501-517Article in journal (Refereed) Published
Abstract [en]

A one-dimensional steady-state advection-diffusion problem using summation-by-parts operators is investigated. For approximating the second derivative, a wide stencil is used, which simplifies implementation and stability proofs. However, it also introduces spurious, oscillating, modes for all mesh sizes. We prove that the size of the spurious modes is equal to the size of the truncation error for a stable approximation and hence disappears with the convergence rate. The theoretical results are verified with numerical experiments.

Place, publisher, year, edition, pages
Wiley-Blackwell, 2018. Vol. 34, no 2, p. 501-517
Keywords [en]
oscillating solutions, spurious solutions, summation-by-parts
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-141208DOI: 10.1002/num.22210ISI: 000423435500006Scopus ID: 2-s2.0-85030173752OAI: oai:DiVA.org:liu-141208DiVA, id: diva2:1144715
Note

Funding agencies:This project was funded by the Swedishe-science Research Center (SeRC). Thefunding source had no involvement in thestudy design, collection and analysis ofdata, or in writing and submitting thisarticle

Available from: 2017-09-27 Created: 2017-09-27 Last updated: 2018-06-01Bibliographically approved

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The full text will be freely available from 2018-09-22 10:34
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Frenander, HannesNordström, Jan
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  • Other style
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  • de-DE
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