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.
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Communicated by: Alexander Barnett
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Eidnes, S., Owren, B. & Ringholm, T. Adaptive energy preserving methods for partial differential equations. Adv Comput Math 44, 815–839 (2018). https://doi.org/10.1007/s10444-017-9562-8
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DOI: https://doi.org/10.1007/s10444-017-9562-8
Keywords
- Energy preserving methods
- Partition of unity method
- Finite difference method
- Adaptive methods
- Moving mesh method