Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Mathematics of Computation
Multi-adaptive time integration
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Relaxed High Resolution Schemes for Hyperbolic Conservation Laws
Journal of Scientific Computing
Moving mesh methods with locally varying time steps
Journal of Computational Physics
Optimistic Parallel Discrete Event Simulations of Physical Systems Using Reverse Computation
Proceedings of the 19th Workshop on Principles of Advanced and Distributed Simulation
Journal of Computational Physics
Self-adaptive time integration of flux-conservative equations with sources
Journal of Computational Physics
Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping
Journal of Scientific Computing
Journal of Computational Physics
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
Journal of Computational Physics
Journal of Computational Physics
An adaptive multiresolution scheme with local time stepping for evolutionary PDEs
Journal of Computational Physics
Algorithms and Data Structures for Multi-Adaptive Time-Stepping
ACM Transactions on Mathematical Software (TOMS)
Compact integration factor methods for complex domains and adaptive mesh refinement
Journal of Computational Physics
An efficient local time-stepping scheme for solution of nonlinear conservation laws
Journal of Computational Physics
Adaptive Timestep Control for Nonstationary Solutions of the Euler Equations
SIAM Journal on Scientific Computing
Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales
Journal of Scientific Computing
Journal of Computational Physics
High-Order Local Time Stepping on Moving DG Spectral Element Meshes
Journal of Scientific Computing
Time asynchronous relative dimension in space method for multi-scale problems in fluid dynamics
Journal of Computational Physics
Journal of Computational Physics
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We develop upwind methods which use limited high resolution corrections in the spatial discretization and local time stepping for forward Euler and second order time discretizations. $L^\infty$ stability is proven for both time stepping schemes for problems in one space dimension. These methods are restricted by a local CFL condition rather than the traditional global CFL condition, allowing local time refinement to be coupled with local spatial refinement. Numerical evidence demonstrates the stability and accuracy of the methods for problems in both one and two space dimensions.