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Adaptive energy preserving methods for partial differential equations

Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2498998
Date
2017
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  • Institutt for matematiske fag [1456]
  • Publikasjoner fra CRIStin - NTNU [21889]
Original version
Advances in Computational Mathematics. 2017, 1-25.   10.1007/s10444-017-9562-8
Abstract
A framework for constructing integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The approach can be used with both finite difference and partition of unity methods, thereby including finite element methods. The schemes are then extended to accommodate r-, h- and p-adaptivity. To illustrate the ideas, the method is applied to the Korteweg–de Vries equation and the sine-Gordon equation. Results from numerical experiments are presented.
Publisher
Springer Verlag
Journal
Advances in Computational Mathematics

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