Petrov-Galerkin flux upwinding for mixed mimetic spectral elements, and its application to geophysical flow problems

DOI10.1016/j.camwa.2021.02.017OpenAlexW3089183775MaRDI QIDQ2019571

Yanyan Li

Publication date: 21 April 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.13225

zbMATH Keywords

mixed finite elementsadvectionupwindingcompatiblemimetic

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Meteorology and atmospheric physics (86A10)

Related Items (5)

Exact spatial and temporal balance of energy exchanges within a horizontally explicit/vertically implicit non-hydrostatic atmosphere ⋮ Compatible finite element methods for geophysical fluid dynamics ⋮ Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics ⋮ Energy conserving SUPG methods for compatible finite element schemes in numerical weather prediction ⋮ Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Cites Work

• A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• The variational multiscale method -- a paradigm for computational mechanics
• Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
• A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations
• A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere
• Impact and importance of hyperdiffusion on the spectral element method: a linear dispersion analysis
• A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition
• An energetically balanced, quasi-Newton integrator for non-hydrostatic vertical atmospheric dynamics
• Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations
• Dispersion analysis of compatible Galerkin schemes for the 1D shallow water model
• Variational multiscale stabilization of high-order spectral elements for the advection-diffusion equation
• Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows
• Edge Functions for Spectral Element Methods
• Efficient Assembly of $H(\mathrm{div})$ and $H(\mathrm{curl})$ Conforming Finite Elements
• Numerical Methods for Fluid Dynamics
• Conservative Multimoment Transport along Characteristics for Discontinuous Galerkin Methods
• Mimetic Spectral Element Advection

This page was built for publication: Petrov-Galerkin flux upwinding for mixed mimetic spectral elements, and its application to geophysical flow problems