Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Higher-order finite elements with mass-lumping for the 1D wave equation
Finite Elements in Analysis and Design - Special issue: selection of papers presented at ICOSAHOM'92
Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Conservative space-time mesh refinement methods for the FDTD solution of Maxwell's equations
Journal of Computational Physics
Journal of Scientific Computing
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
Journal of Computational and Applied Mathematics
Multirate Timestepping Methods for Hyperbolic Conservation Laws
Journal of Scientific Computing
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Multirate Explicit Adams Methods for Time Integration of Conservation Laws
Journal of Scientific Computing
The Mortar-Discontinuous Galerkin Method for the 2D Maxwell Eigenproblem
Journal of Scientific Computing
Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation
Journal of Scientific Computing
Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations
SIAM Journal on Scientific Computing
Locally implicit discontinuous Galerkin method for time domain electromagnetics
Journal of Computational Physics
Local time stepping and discontinuous Galerkin methods for symmetric first order hyperbolic systems
Journal of Computational and Applied Mathematics
Explicit local time-stepping methods for Maxwell's equations
Journal of Computational and Applied Mathematics
High-Order Local Time Stepping on Moving DG Spectral Element Meshes
Journal of Scientific Computing
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Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps precisely where the smallest elements in the mesh are located. Starting from classical Adams-Bashforth multi-step methods, local time-stepping methods of arbitrarily high order of accuracy are derived for damped wave equations. When combined with a finite element discretization in space with an essentially diagonal mass matrix, the resulting time-marching schemes are fully explicit and thus inherently parallel. Numerical experiments with continuous and discontinuous Galerkin finite element discretizations corroborate the expected rates of convergence and illustrate the usefulness of these local time-stepping methods.