Adaptive energy preserving methods for partial differential equations
Journal article, Peer reviewed
MetadataShow full item record
Original versionAdvances in Computational Mathematics. 2017, 1-25. 10.1007/s10444-017-9562-8
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.