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Revisiting and Extending Interface Penalties for Multidomain Summation-by-Parts Operators
NASA Langley Research Center.
Uppsala universitet, Avdelningen för teknisk databehandling.ORCID iD: 0000-0002-7972-6183
Brown University.
2010 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 45, no 1-3, 118-150 p.Article in journal (Refereed) Published
Abstract [en]

A general interface procedure is presented for multi-domain collocation methods satisfying the summation-by-parts (SBP) spatial discretization convention. Unlike more traditional operators (e.g. FEM) applied to the advection-diffusion equation, the new procedure penalizes the solution and the first p derivatives across the interface. The combined interior/interface operators are proven to be pointwise stable, and conservative, although accuracy deteriorates for p≥2. Penalties between two different sets of variables are compared (motivated by FEM primal and flux formulations), and are shown to be equivalent for certain choices of penalty parameters. Extensive validation studies are presented using two classes of high-order SBP operators: (1) central finite difference, and (2) Legendre spectral collocation.

Place, publisher, year, edition, pages
Springer , 2010. Vol. 45, no 1-3, 118-150 p.
Keyword [en]
Summation-by-parts (SBP) - High-order finite difference - Finite element - DG - Numerical stability - Interface conditions - Conservation - Applied and numerical mathematics
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-68529DOI: 10.1007/s10915-009-9301-5ISI: 000281250600007OAI: diva2:418978
The original publication is available at Mark H. Carpenter, Jan Nordström and David Gottlieb, Revisiting and Extending Interface Penalties for Multidomain Summation-by-Parts Operators, 2010, Journal of Scientific Computing, (45), 118-150. Copyright: Springer Science Business Media Available from: 2009-07-22 Created: 2011-05-24 Last updated: 2013-08-30

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