38 citations · 81 across the 15 of their papers we have counts for
5 papers · 1 filter
Invariant Variational Schemes for Ordinary Differential Equations
Alex Bihlo, James Jackaman, Francis Valiquette
We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variat…
On the development of symmetry-preserving finite element schemes for ordinary differential equations
Alex Bihlo, James Jackaman, Francis Valiquette
In this paper we introduce a procedure, based on the method of equivariant moving frames, for formulating continuous Galerkin finite element schemes that preserve the Lie point sym…
Symmetry-preserving finite element schemes: An introductory investigation
Alexander Bihlo, Francis Valiquette
Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations.…
Symmetry-preserving numerical schemes
Alexander Bihlo, Francis Valiquette
In these lectures we review two procedures for constructing finite difference numerical schemes that preserve symmetries of differential equations. The first approach is based on L…
Invariant Discretization of Partial Differential Equations Admitting Infinite-Dimensional Symmetry Groups
Raphael Rebelo, Francis Valiquette
Given a differential equation with infinite-dimensional symmetry pseudo-group it is shown, using an example, that it is generally not possible to construct enough joint invariants…