Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws
SIAM Journal on Scientific Computing
New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
High-Resolution Nonoscillatory Central Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
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In this paper we present, analyze and implement a new local piecewise parabolic method for nonlinear Hamilton-Jacobi equations. The scheme is third-order accurate in smooth regions, uses a concept of local smoothing to prevent the excessive increase of the total variation at discontinuity, and has a local stencil in the sense that it does not extrapolate from data of the smoothest neighboring cells. One and two-dimensional numerical experiments, accuracy tests, and the behavior of the total variation of the approximate solution are presented to prove the accuracy and good resolution of our method.