We give the first convergence proof for the Lax-Friedrichs finite difference scheme for non-convex genuinely nonlinear scalar conservation laws of the form ut + f(k(x, t), u)x = 0, where the coefficient k(x, t) is allowed to be discontinuous along curves in the (x, t) plane. In contrast to most of the existing literature on problems with discontinuous coefficients, our convergence proof is not ...

Efficient and dexterous manipulation of very small (micrometer and millimeter sized) objects require the use of high precision micromanipulation systems. The accuracy of the positioning is nevertheless limited by the noise due to vibrations of the end effectors making it difficult to achieve precise micrometer and nanometer displacements to grip small objects. The purpose of this paper is to an...

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high accuracy at a fraction of the cost volume WENO or DG scheme comparable accuracy. This makes them quite attractive several science and engineering applications. But, to best our knowledge, such not extended non-linear hyper...

We propose a high order finite difference linear scheme combined with bound preserving maximum-principle-preserving (MPP) flux limiter to solve the incompressible flow system. For such problem highly oscillatory structure but not strong shocks, our approach seems be less dissipative and much costly than WENO type scheme, has resolution due Hermite reconstruction. Spurious numerical oscillations...