Construction of simple, stable, and convergent high order schemes for stead y first order Hamilton-Jacobi equations

摘要

We develop a very simple algorithm that permits to construct compact, high order schemes for steady first order Hamilton-Jacobi equations. The algorithm relies on the blending of a first order scheme and a compact high order scheme. The blending is conducted in such a way that the scheme is formally high order accurate. A convergence proof without error estimate is given. We provide several numerical illustrations that demonstrate the effective accuracy of the scheme. The numerical examples use triangular unstructured meshes, but our method may be applied to other kind of meshes. Several implementation remarks are also given.