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SIAM J. SCI. COMPUT. c 2009 Society for Industrial and Applied Mathematics
Vol. 31, No. 4, pp. 24192446
CONSTRUCTION OF SIMPLE, STABLE, AND CONVERGENT
HIGH ORDER SCHEMES FOR STEADY FIRST ORDER
HAMILTONJACOBI EQUATIONS
R. ABGRALL
Abstract. We develop a very simple algorithm that permits to construct compact, high order
schemes for steady first order HamiltonJacobi 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.
Key words. HamiltonJacobi, unstructured meshes, high order schemes
AMS subject classifications. 65M60, 35L60, 65M12, 49L25
DOI. 10.1137/040615997
1. Introduction. We consider the following Cauchy problem: find u C0
(),
the space of continuous function on the open subset Rd
