Journal of Computational Physics
A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations
Journal of Scientific Computing
A forward-trajectory global semi-Lagrangian transport scheme
Journal of Computational Physics
A spectral element semi-Lagrangian (SESL) method for the spherical shallow water equations
Journal of Computational Physics
Nonlinear operator integration factor splitting for the shallow water equations
Applied Numerical Mathematics
Adaptive Atmospheric Modeling: Scientific Computing at Its Best
Computing in Science and Engineering
Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows
Journal of Scientific Computing
A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows
Journal of Computational Physics
Hybrid Eulerian-Lagrangian Semi-Implicit Time-Integrators
Computers & Mathematics with Applications
Asset pricing with dynamic programming
Computational Economics
ACM Transactions on Graphics (TOG)
A regularized Lagrangian finite point method for the simulation of incompressible viscous flows
Journal of Computational Physics
A velocity decomposition approach for moving interfaces in viscous fluids
Journal of Computational Physics
Nonlinear operator integration factor splitting for the shallow water equations
Applied Numerical Mathematics
Applied Numerical Mathematics
Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of HJB PDEs
SIAM Journal on Control and Optimization
Journal of Scientific Computing
Journal of Computational Physics
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The convergence properties of a class of high-order semi-Lagrangian schemes for pure advection equations are studied here in the framework of the theory of viscosity solutions. We review the general convergence results for discrete-time approximation schemes belonging to that class and we prove some a priori estimates in $L^\infty$ and L2 for the rate of convergence of fully discrete schemes. We prove then that a careful coupling of time and space discretizations can allow large time steps in the numerical integration still preserving the accuracy of the solutions. Several examples of schemes and numerical tests are presented.