22 citations · 45 across the 14 of their papers we have counts for
8 papers · 1 filter
Derivative-free discrete gradient methods
Håkon Noren Myhr, Sølve Eidnes
Discrete gradient methods are a class of numerical integrators producing solutions with exact preservation of first integrals of ordinary differential equations. In this paper, we…
Order theory for discrete gradient methods
Sølve Eidnes
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we…
Linearly implicit local and global energy-preserving methods for PDEs with a cubic Hamiltonian
Sølve Eidnes, Lu Li
We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multi-symplectic PDEs with cubic invariants. The methods…
Linearly implicit structure-preserving schemes for Hamiltonian systems
Sølve Eidnes, Lu Li, Shun Sato
Kahan's method and a two-step generalization of the discrete gradient method are both linearly implicit methods that can preserve a modified energy for Hamiltonian systems with a c…
Energy preserving methods on Riemannian manifolds
Elena Celledoni, Sølve Eidnes, Brynjulf Owren +1
The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a r…
Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows
Elena Celledoni, Sølve Eidnes, Brynjulf Owren +1
This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative…
Energy preserving moving mesh methods applied to the BBM equation
Sølve Eidnes, Torbjørn Ringholm
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 w…
Adaptive Energy Preserving Methods for Partial Differential Equations
Sølve Eidnes, Brynjulf Owren, Torbjørn Ringholm
A method for constructing first integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The method can be used wi…