Least-squares finite element methods (LSFEMs) for the inviscid Burgers equation are studied. The scalar nonlinear hyperbolic conservation law is reformulated by introducing the flux vector, or the associated flux potential, explicitly as additional dependent variables. This reformulation highlights the smoothness of the flux vector for weak solutions, namely f(u) ∈ H(div,Ω). The standard least-...

We present a (partial) historical summary of the mathematical analysis finite difference and volume methods, paying special attention to Lax–Richtmyer Lax–Wendroff theorems. then state consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates recent generalization flux notion designed cope with general discrete functions.

A parallel Hopscotch algorithm for the simulation of semiconductor laser arrays which overlaps the computations and communications is presented. The method uses a Lax-Wendroff scheme for the hyperbolic part of the operators and allows to obtain near-to-perfect speed-ups on MIMD computers. Numerical experiments indicate that semiconductor laser arrays exhibit a rich dynamic behavior ranging from...

2.1 Examples of conservative schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 The Godunov Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2 The Lax-Friedrichs Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 The local Lax-Friedrichs Scheme . . . . . . . ....

This paper provides a direct equivalence proof for minimax solutions of A.I. Subbotin and generalized weak solutions in the sense of idempotent analysis. It is shown that the Hamilton-Jacobi equation Vt+H(t, x,DxV ) = 0 (with the Hamiltonian H(t, x, s) concave in s), considered in the context of minimax generalized solutions, is linear w.r.t. ⊕ = min and ̄ = +. This leads to a representation fo...

In this paper, we consider linear stability issues for one-dimensional hyperbolic conservation laws using a class of conservative high order upwind-biased finite difference schemes, which is a prototype for the weighted essentially non-oscillatory (WENO) schemes, for initial-boundary value problems (IBVP). The inflow boundary is treated by the so-called inverse Lax-Wendroff (ILW) or simplified ...

In this paper, we analyze the Lax-Wendroff discontinuous Galerkin (LWDG) method for solving linear conservation laws. The method was originally proposed by Guo et al. in [11], where they applied local discontinuous Galerkin (LDG) techniques to approximate high order spatial derivatives in the Lax-Wendroff time discretization. We show that, under the standard CFL condition τ ≤ λh (where τ and h ...

Based on general partitions of unity and standard numerical flux functions, a class of mesh-free methods for conservation laws is derived. A Lax-Wendroff type consistency analysis is carried out for the general case of moving partition functions. The analysis leads to a set of conditions which are checked for the finite volume particle method FVPM. As a by-product, classical finite volume schem...