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Variational discretizations of viscous and resistive magnetohydrodynamics using structure-preserving finite elements
Valentin Carlier
We propose a novel structure preserving discretization for viscous and resistive magnetohydrodynamics. We follow the recent line of work on discrete least action principle for flui…
Variational discretizations of ideal magnetohydrodynamics in smooth regime using finite element exterior calculus
Valentin Carlier, Martin Campos-Pinto
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for flu…
Mass, momentum and energy preserving FEEC and broken-FEEC schemes for the incompressible Navier-Stokes equations
Valentin Carlier, Martin Campos Pinto, Francesco Fambri
In this article we propose two finite element schemes for the Navier-Stokes equations, based on a reformulation that involves differential operators from the de Rham sequence and a…
Invariant domain preserving high-order spectral discontinuous approximations of hyperbolic systems
Florent Renac, Valentin Carlier
We propose a limiting procedure to preserve invariant domains with time explicit discrete high-order spectral discontinuous approximate solutions to hyperbolic systems of conservat…