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A stable and dual consistent boundary treatment using finite differences on summation-by-parts form
Uppsala University, Department of Information Technology.
Linköpings universitet, Matematiska institutionen, Beräkningsmatematik. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0002-7972-6183
2012 (engelsk)Inngår i: European Congress on Computational Methods in Applied Sciences and Engineering, Vienna University of Technology , 2012Konferansepaper, Publicerat paper (Annet vitenskapelig)
Abstract [en]

This paper is concerned with computing very high order accurate linear functionals from a numerical solution of a time-dependent partial differential equation (PDE). Based on finite differences on summation-by-parts form, together with a weak implementation of the boundary conditions, we show how to construct suitable boundary conditions for the PDE such that the continuous problem is well-posed and the discrete problem is stable and spatially dual consistent. These two features result in a superconvergent functional, in the sense that the order of accuracy of the functional is provably higher than that of the solution.

sted, utgiver, år, opplag, sider
Vienna University of Technology , 2012.
Emneord [en]
Superconvergence, functionals, summation-by-parts, weak boundary conditions, stability, dual consistency
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-81890ISBN: 978-3-9503537-0-9 (tryckt)OAI: oai:DiVA.org:liu-81890DiVA, id: diva2:556560
Konferanse
(ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.) Vienna, Austria, September 10-14, 2012
Tilgjengelig fra: 2012-09-25 Laget: 2012-09-24 Sist oppdatert: 2016-09-09

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