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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.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2012 (English)In: European Congress on Computational Methods in Applied Sciences and Engineering, Vienna University of Technology , 2012Conference paper (Other academic)
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.

Place, publisher, year, edition, pages
Vienna University of Technology , 2012.
Keyword [en]
Superconvergence, functionals, summation-by-parts, weak boundary conditions, stability, dual consistency
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-81890ISBN: 978-3-9503537-0-9OAI: diva2:556560
(ECCOMAS 2012) J. Eberhardsteiner (eds.) Vienna, Austria, September 10-14, 2012
Available from: 2012-09-25 Created: 2012-09-24 Last updated: 2016-09-09

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