On the stability of the flux reconstruction schemes on quadrilateral elements for the linear advection equation

DOI10.1007/S10915-015-0102-8zbMath1341.65035OpenAlexW3003345438MaRDI QIDQ292577

Abhishek Sheshadri, Anthony Jameson

Publication date: 8 June 2016

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-015-0102-8

zbMATH Keywords

stabilityconservation lawhigh-order methodslinear advection equationflux reconstructionLax-Friedrichs formulationmodified Sobolev normnodal discontinuous Galerkin methodquadrilateralsuniform Cartesian mesh

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (10)

A new norm and stability condition for tensor product flux reconstruction schemes ⋮ A flux reconstruction kinetic scheme for the Boltzmann equation ⋮ Nonlinearly stable flux reconstruction high-order methods in split form ⋮ Effect of mesh quality on flux reconstruction in multi-dimensions ⋮ Provably stable flux reconstruction high-order methods on curvilinear elements ⋮ An extended range of stable flux reconstruction schemes on quadrilaterals for various polynomial bases ⋮ Effective high-order energy stable flux reconstruction methods for first-order hyperbolic linear and nonlinear systems ⋮ ZEFR: a GPU-accelerated high-order solver for compressible viscous flows using the flux reconstruction method ⋮ An analysis of stability of the flux reconstruction formulation on quadrilateral elements for the linear advection-diffusion equation ⋮ The flux reconstruction method with Lax-Wendroff type temporal discretization for hyperbolic conservation laws

Cites Work

• Unnamed Item
• Energy stable flux reconstruction schemes for advection-diffusion problems on triangles
• On the non-linear stability of flux reconstruction schemes
• Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations
• A new class of high-order energy stable flux reconstruction schemes for triangular elements
• Energy stable flux reconstruction schemes for advection-diffusion problems on tetrahedra
• A proof of the stability of the spectral difference method for all orders of accuracy
• A new class of high-order energy stable flux reconstruction schemes
• A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids
• A conservative staggered-grid Chebyshev multidomain method for compressible flows
• High-order flux reconstruction schemes with minimal dispersion and dissipation
• Spectral difference method for unstructured grids. I. Basic formulation
• Connections between the discontinuous Galerkin method and high‐order flux reconstruction schemes
• Spectral/hp Element Methods for Computational Fluid Dynamics

This page was built for publication: On the stability of the flux reconstruction schemes on quadrilateral elements for the linear advection equation