Stochastic and variational approach to the Lax-Friedrichs scheme

More on stochastic and variational approach to the Lax-Friedrichs scheme

Error Estimates for the Lax — Friedrichs Scheme for Balance Laws

In this paper we extend the result from [9] (V. Jovanović, C. Rohde, Error estimates for finite volume approximations of classical solutions for nonlinear systems of balance laws, SIAM J. Numer. Anal., 43 (2006)), where, among other things, an h — error estimate in the L — norm for the elastodynamics system has been established. We first derive the general error estimate from [9, Theorem 4.4] i...

Lax – Friedrichs sweeping scheme for static Hamilton – Jacobi equations q

We propose a simple, fast sweeping method based on the Lax–Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton–Jacobi equations in any number of spatial dimensions. By using the Lax–Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss–Seidel type nonlinear ite...

Two-step Lax-Friedrichs method

The Lax-Friedrichs (LxF) method [2, 3, 4] is a basic method for the solution of hyperbolic partial differential equations (PDEs). Its use is limited because its order is only one, but it is easy to program, applicable to general PDEs, and has good qualitative properties because it is monotone. The LxF method is often used to show the effects of dissipation, but it is not actually a dissipative ...

On the Stability of Friedrichs' Scheme and the Modified Lax-Wendroff Scheme*

Necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme with smooth coefficients are derived by means of Kreiss' Matrix Theorem and the first Stability Theorem of Lax and Nirenberg. In this note we derive necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme [8] for the hyperbolic system n (1) ". =...