Adaptive energy preserving methods for partial differential equations
Journal article, Peer reviewed
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Date
2017Metadata
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- Institutt for matematiske fag [2533]
- Publikasjoner fra CRIStin - NTNU [38576]
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.