On the eigenvalues of the ADER-WENO Galerkin predictor

DOI10.1016/j.jcp.2016.12.058zbMath1380.65269arXiv1611.09153OpenAlexW2569417348MaRDI QIDQ1685191

Haran Jackson

Publication date: 13 December 2017

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.09153

zbMATH Keywords

convergenceeigenvaluesGalerkinADER-WENO

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (14)

High order direct arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes ⋮ Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure ⋮ An arbitrary high-order spectral difference method for the induction equation ⋮ The Montecinos-Balsara ADER-FV polynomial basis: convergence properties \& extension to non-conservative multidimensional systems ⋮ Continuous Finite Element Subgrid Basis Functions for Discontinuous Galerkin Schemes on Unstructured Polygonal Voronoi Meshes ⋮ A fast numerical scheme for the Godunov-Peshkov-Romenski model of continuum mechanics ⋮ ADER discontinuous Galerkin Material Point Method ⋮ Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows ⋮ High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves ⋮ The simple finite volume Lax-Wendroff weighted essentially nonoscillatory schemes for shallow water equations with bottom topography ⋮ Stability analysis and improvement of the solution reconstruction for cell-centered finite volume methods on unstructured meshes ⋮ DeC and ADER: similarities, differences and a unified framework ⋮ Efficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engine ⋮ An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density

Uses Software

• HE-E1GODF

Cites Work

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• ADER-WENO finite volume schemes with space-time adaptive mesh refinement
• High order space-time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems
• Very high order \(P_NP_M\) schemes on unstructured meshes for the resistive relativistic MHD equations
• A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
• Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magneto\-hydrodynamics
• ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows
• Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes -- speed comparisons with Runge-Kutta methods
• Riemann Solvers and Numerical Methods for Fluid Dynamics

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