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Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form
Uppsala University, Department of Information Technology, Sweden.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2012 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, no 20, 6846-6860 p.Article in journal (Refereed) Published
Abstract [en]

Finitedifference operators satisfying the summation-by-parts (SBP) rules can be used to obtain high order accurate, energy stable schemes for time-dependent partial differential equations, when the boundary conditions are imposed weakly by the simultaneous approximation term (SAT).

In general, an SBP-SAT discretization is accurate of order p + 1 with an internal accuracy of 2p and a boundary accuracy of p. Despite this, it is shown in this paper that any linear functional computed from the time-dependent solution, will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way.

The method does not involve the solution of the dual equations, and superconvergent functionals are obtained at no extra computational cost. Four representative model problems are analyzed in terms of convergence and errors, and it is shown in a systematic way how to derive schemes which gives superconvergentfunctionaloutputs.

Place, publisher, year, edition, pages
ACM Press, 2012. Vol. 231, no 20, 6846-6860 p.
Keyword [en]
High order finitedifferences; Summation-by-parts; Superconvergence; Time-dependentfunctionaloutput; Dual consistency; Stability
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-80849DOI: 10.1016/ 000307299400014OAI: diva2:548612

funding agencies|SNIC through Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX)|p2010056|European Commission|ACP0-GA-2010-265780|

Available from: 2012-08-31 Created: 2012-08-31 Last updated: 2013-08-30

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