Weighted ENO Schemes for Hamilton--Jacobi Equations
2000; Society for Industrial and Applied Mathematics; Volume: 21; Issue: 6 Linguagem: Inglês
10.1137/s106482759732455x
ISSN1095-7197
AutoresGuang-Shan Jiang, Danping Peng,
Tópico(s)Advanced Thermodynamics and Statistical Mechanics
ResumoIn this paper, we present a weighted ENO (essentially nonoscillatory) scheme to approximate the viscosity solution of the Hamilton--Jacobi equation: $$ \phi_t + H(x_1,\ldots,x_d,t,\phi,\phi_{x_1},\ldots,\phi_{x_d}) = 0. $$ This weighted ENO scheme is constructed upon and has the same stencil nodes as the third order ENO scheme but can be as high as fifth order accurate in the smooth part of the solution. In addition to the accuracy improvement, numerical comparisons between the two schemes also demonstrate that the weighted ENO scheme is more robust than the ENO scheme.
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