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Summation-By-Parts Operators for Time Discretisation: Initial Investigations
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
2012 (English)Report (Other academic)
Abstract [en]

We develop a new high order accurate time-discretisation technique for initial value problems. We focus on problems that originate from a space discretisation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the time-domain. The new time-discretisation method is global and together with the approximation in space, it generates optimal fully discrete energy estimates, and efficient methods for both stiff and non-stiff problems. In particular, it is shown how stable fully discrete high order accurate approximations of the Maxwells’ equations, the elastic wave equations and the linearised Euler and Navier-Stokes equations are obtained. Even though we focus on finite difference approximations, we stress that the methodology is completely general and suitable for all semi-discrete energy-stable approximations.

Place, publisher, year, edition, pages
2012. , 27 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2012/08
Keyword [en]
Time integration, initial value problems, weak initial conditions, high order accuracy, initial value boundary problems, weak boundary conditions, global methods, stability, convergence, summation-by-parts operators, energy estimates, stiff problems
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-79325OAI: diva2:540404
Available from: 2012-07-10 Created: 2012-07-10 Last updated: 2013-08-30Bibliographically approved

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