Relaxing the CFL condition for the wave equation on adaptive meshes

DOI10.1007/s10915-017-0394-yzbMath1378.65169arXiv1601.04812OpenAlexW2964082690MaRDI QIDQ2412738

Daniel Peterseim, Mira Schedensack

Publication date: 27 October 2017

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

Full work available at URL: https://arxiv.org/abs/1601.04812

zbMATH Keywords

stabilityconvergencewave equationfinite element methodadaptive mesh refinementCourant-Friedrichs-Lewy conditionhyperbolic equationnumerical homogenisationexplicit leapfrog method

Mathematics Subject Classification ID

Wave equation (35L05) 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)

Related Items (14)

Numerical homogenization beyond scale separation ⋮ Numerical Upscaling for Wave Equations with Time-Dependent Multiscale Coefficients ⋮ Adaptive Isogeometric Phase-Field Modeling of Weak and Strong Discontinuities ⋮ Numerical Homogenization of H(curl)-Problems ⋮ Multiscale scattering in nonlinear Kerr-type media ⋮ On the stability of the Rayleigh-Ritz method for eigenvalues ⋮ A Space-Time Multiscale Method for Parabolic Problems ⋮ Neural Network Approximation of Coarse-Scale Surrogates in Numerical Homogenization ⋮ Multiscale methods for solving wave equations on spatial networks ⋮ Efficient implementation of the localized orthogonal decomposition method ⋮ Explicit computational wave propagation in micro-heterogeneous media ⋮ A PDE approach to fractional diffusion: a space-fractional wave equation ⋮ A Priori Error Analysis of a Numerical Stochastic Homogenization Method ⋮ Superconvergence of time invariants for the Gross–Pitaevskii equation

Cites Work

• Unnamed Item
• Unnamed Item
• Mathematical aspects of discontinuous Galerkin methods.
• Computation of eigenvalues by numerical upscaling
• On a BPX-preconditioner for P1 elements
• The singular complement method for 2d scalar problems
• Multi-level explicit local time-stepping methods for second-order wave equations
• Finite elements with mesh refinement for wave equations in polygons
• On the stability of the Rayleigh-Ritz method for eigenvalues
• Two-Level Discretization Techniques for Ground State Computations of Bose-Einstein Condensates
• Localized orthogonal decomposition method for the wave equation with a continuum of scales
• Variational Multiscale Stabilization and the Exponential Decay of Fine-Scale Correctors
• Generalized finite element methods for quadratic eigenvalue problems
• Localization of elliptic multiscale problems
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations
• Foundations of Finite Element Methods for Wave Equations of Maxwell Type
• Convergence rates for adaptive finite elements
• Realistic Eigenvalue Bounds for the Galerkin Mass Matrix
• An Optimal Order Process for Solving Finite Element Equations
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• L²best approximation of the elastic stress in the Arnold–Winther FEM
• Two-level additive Schwarz preconditioners for nonconforming finite element methods
• Finite element quasi-interpolation and best approximation
• Convergence of a Discontinuous Galerkin Multiscale Method
• Oversampling for the Multiscale Finite Element Method
• The Mathematical Theory of Finite Element Methods
• Multiscale Partition of Unity

This page was built for publication: Relaxing the CFL condition for the wave equation on adaptive meshes