Energy preserving moving mesh methods applied to the BBM equation
For researchers in numerical PDEs, this provides a way to preserve energy exactly in moving mesh simulations, though it is an incremental extension of existing methods.
The authors developed energy-preserving numerical methods for PDEs using partition of unity and extended them to moving meshes via rezoning, applied to the BBM equation. Numerical experiments showed advantages of the methods.
Energy preserving numerical methods for a certain class of PDEs are derived, applying the partition of unity method. The methods are extended to also be applicable in combination with moving mesh methods by the rezoning approach. These energy preserving moving mesh methods are then applied to the Benjamin--Bona--Mahony equation, resulting in schemes that exactly preserve an approximation to one of the Hamiltonians of the system. Numerical experiments that demonstrate the advantages of the methods are presented.