11 citations · 11 across the 3 of their papers we have counts for
5 papers
HDG methods in finite element exterior calculus
Calvin Reedy, Ari Stern, Yunhui Xue
We develop and analyze HDG methods for two central problems in finite element exterior calculus, the Hodge-Dirac problem and the Hodge-Laplace problem, in arbitrary dimension .…
Finite element exterior calculus for time-dependent Hamiltonian partial differential equations
Ari Stern, Enrico Zampa
The success of symplectic integrators for Hamiltonian ODEs has led to a decades-long program of research seeking analogously structure-preserving numerical methods for Hamiltonian…
Quadratic projectable Runge-Kutta methods
Ari Stern, Milo Viviani
Runge-Kutta methods are affine equivariant: applying a method before or after an affine change of variables yields the same numerical trajectory. However, for some applications, on…
Multisymplecticity in finite element exterior calculus
Ari Stern, Enrico Zampa
We consider the application of finite element exterior calculus (FEEC) methods to a class of canonical Hamiltonian PDE systems involving differential forms. Solutions to these syst…
Projection methods and discrete gradient methods for preserving first integrals of ODEs
R. A. Norton, D. I. McLaren, G. R. W. Quispel +2
In this paper we study linear projection methods for approximating the solution and simultaneously preserving first integrals of autonomous ordinary differential equations. We show…