A quasi-Hamiltonian discretization of the thermal shallow water equations
C Eldred, T Dubos, E Kritsikis - Journal of Computational Physics, 2019 - Elsevier
The rotating shallow water (RSW) equations are the usual testbed for the development of
numerical methods for three-dimensional atmospheric and oceanic models. However, an …
numerical methods for three-dimensional atmospheric and oceanic models. However, an …
A variational finite-element discretization approach for perfect incompressible fluids
We propose a finite-element discretization approach for the incompressible Euler equations
which mimics their geometric structure and their variational derivation. In particular, we …
which mimics their geometric structure and their variational derivation. In particular, we …
A structure preserving numerical method for the ideal compressible MHD system
We introduce a novel structure-preserving method in order to approximate the compressible
ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD …
ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD …
A stable mimetic finite-difference method for convection-dominated diffusion equations
Convection-diffusion equations arise in a variety of applications such as particle transport,
electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated …
electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated …
A Hybridizable Discontinuous Galerkin Method for Magnetic Advection–Diffusion Problems
J Wang, S Wu - Journal of Scientific Computing, 2024 - Springer
We propose and analyze a hybridizable discontinuous Galerkin (HDG) method for solving a
mixed magnetic advection–diffusion problem within a more general Friedrichs system …
mixed magnetic advection–diffusion problem within a more general Friedrichs system …
Simplex-Averaged Finite Element Methods for (grad), (curl), and (div) Convection-Diffusion Problems
This paper is devoted to the construction and analysis of the finite element approximations
for the H(D) convection-diffusion problems, where D can be chosen as grad, curl, or div in …
for the H(D) convection-diffusion problems, where D can be chosen as grad, curl, or div in …
Discontinuous Galerkin methods for magnetic advection-diffusion problems
J Wang, S Wu - arXiv preprint arXiv:2208.01267, 2022 - arxiv.org
We devise and analyze a class of the primal discontinuous Galerkin methods for the
magnetic advection-diffusion problems based on the weighted-residual approach. In …
magnetic advection-diffusion problems based on the weighted-residual approach. In …
[PDF][PDF] Computational magnetohydrodynamics with discrete differential forms
C Pagliantini - 2016 - research-collection.ethz.ch
The equations of magnetohydrodynamics (MHD) model the interaction of conducting fluids
with electromagnetic fields, and provide the mathematical description of problems arising in …
with electromagnetic fields, and provide the mathematical description of problems arising in …
An asymptotic-preserving and exactly mass-conservative semi-implicit scheme for weakly compressible flows based on compatible finite elements
We present a novel asymptotic-preserving semi-implicit finite element method for weakly
compressible and incompressible flows based on compatible finite element spaces. The …
compressible and incompressible flows based on compatible finite element spaces. The …
An edge-based scheme on polyhedral meshes for vector advection-reaction equations
P Cantin, A Ern - ESAIM: Mathematical Modelling and Numerical …, 2017 - esaim-m2an.org
We devise and analyze an edge-based scheme on polyhedral meshes to approximate a
vector advection-reaction problem. The well-posedness of the discrete problem is analyzed …
vector advection-reaction problem. The well-posedness of the discrete problem is analyzed …