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21
Central WENO schemes for HamiltonJacobi equations on triangular meshes
 J. Sci. Comput
, 2005
"... Abstract. We derive Godunovtype semidiscrete central schemes for Hamilton–Jacobi equations on triangular meshes. Highorder schemes are then obtained by combining our new numerical fluxes with highorder WENO reconstructions on triangular meshes. The numerical fluxes are shown to be monotone in ce ..."
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Cited by 7 (0 self)
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Abstract. We derive Godunovtype semidiscrete central schemes for Hamilton–Jacobi equations on triangular meshes. Highorder schemes are then obtained by combining our new numerical fluxes with highorder WENO reconstructions on triangular meshes. The numerical fluxes are shown to be monotone
HighOrder Central WENO Schemes for 1D HamiltonJacobi Equations
, 2002
"... this paper we derive fullydiscrete Central WENO (CWENO) schemes for approximating solutions of (1), which combine our previous works [2, 13, 14]. We introduce third and fifthorder accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core ingredi ..."
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Cited by 4 (3 self)
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this paper we derive fullydiscrete Central WENO (CWENO) schemes for approximating solutions of (1), which combine our previous works [2, 13, 14]. We introduce third and fifthorder accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core
Spatially adaptive techniques for level set methods and incompressible flow
 Comput. Fluids
"... Since the seminal work of [92] on coupling the level set method of [69] to the equations for twophase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic handling of topological changes ..."
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Cited by 73 (15 self)
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to both its popularity and stringent accuracy requirements. Thus, we discuss higher order accurate numerical methods such as HamiltonJacobi WENO [46], methods for maintaining a signed distance function, hybrid methods such as the particle level set method [27] and the coupled level set volume of fluid
High Order Fast Sweeping Methods for Static HamiltonJacobi Equations
"... We construct high order fast sweeping numerical methods for computing viscosity solutions of static HamiltonJacobi equations on rectangular grids. These methods combine high order weighted essentially nonoscillatory (WENO) approximation to derivatives, monotone numerical Hamiltonians and Gauss Sei ..."
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Cited by 17 (4 self)
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We construct high order fast sweeping numerical methods for computing viscosity solutions of static HamiltonJacobi equations on rectangular grids. These methods combine high order weighted essentially nonoscillatory (WENO) approximation to derivatives, monotone numerical Hamiltonians and Gauss
Compact central WENO schemes for multidimensional conservation laws
 SIAM J. Sci. Comput
, 2000
"... We present new third and fifthorder Godunovtype central schemes for approximating solutions of the HamiltonJacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greate ..."
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Cited by 60 (12 self)
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is then extended to a multidimensional fifthorder scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes. Key words. HamiltonJacobi equations, central schemes, high order, WENO, CWENO.
A weighted essentially nonoscillatory, large timestep scheme for HamiltonJacobi equations
 SIAM J. Sci. Comput
, 2005
"... Abstract. We investigate the application of weighted essentially nonoscillatory (WENO) reconstructions to a class of semiLagrangian schemes for first order timedependent Hamilton–Jacobi equations. In particular, we derive a general form of the scheme, study sufficient conditions for its convergen ..."
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Cited by 11 (2 self)
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Abstract. We investigate the application of weighted essentially nonoscillatory (WENO) reconstructions to a class of semiLagrangian schemes for first order timedependent Hamilton–Jacobi equations. In particular, we derive a general form of the scheme, study sufficient conditions for its
Essentially nonoscillatory and weighted essentially nonoscillatory schemes for hyperbolic conservation laws
, 1998
"... In these lecture notes we describe the construction, analysis, and application of ENO (Essentially NonOscillatory) and WENO (Weighted Essentially NonOscillatory) schemes for hyperbolic conservation laws and related HamiltonJacobi equations. ENO and WENO schemes are high order accurate nite di ere ..."
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Cited by 270 (26 self)
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In these lecture notes we describe the construction, analysis, and application of ENO (Essentially NonOscillatory) and WENO (Weighted Essentially NonOscillatory) schemes for hyperbolic conservation laws and related HamiltonJacobi equations. ENO and WENO schemes are high order accurate nite di
Numerical Methods for Computing Discontinuous Solutions of aClass of HamiltonJacobi Equations Using aLevel Set Method
"... In this article, we first introduce aLaxFriedrichs type finite difference method to compute the $\mathrm{L}$solution, following its original definition recently proposed by the second auther in[12] using level sets. We then generalize our numerical methods to compute the proper viscosity solution ..."
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general equations developing shocks other than conservation laws. These numerical methods are generalized to higher order accuracy using WENO Local LaxFriedrichs methods [17]. We verify that our numerical solutions approximate the proper viscosity solutions of [11] and, in particular, the entropy
Numerical Methods for Computing Discontinuous Solutions of aClass of HamiltonJacobi Equations Using aLevel Set Method
"... In this article, we first introduce aLaxFriedrichs type finite difference method to compute the $\mathrm{L}$solution, following its original definition recently proposed by the second auther in[12] using level sets. We then generalize our numerical methods to compute the proper viscosity solution ..."
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solutions in case of conservtion laws. 1Introduction Nonlinear HamiltonJacobi Equations arise in many different fields, including control theory, and differential games. Because of the nonlinearity, the Cauchy problems usually have nonclassical solutions due to the crossing of characteristic curves.
Adaptive centralupwind schemes for Hamilton–Jacobi equations with nonconvex Hamiltonians, http://www.math. tulane.edu/~kurganov/pub.html
"... This paper is concerned with computing viscosity solutions of Hamilton–Jacobi equations using highorder Godunovtype projectionevolution methods. These schemes employ piecewise polynomial reconstructions, and it is a wellknown fact that the use of more compressive limiters or higherorder polynom ..."
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Cited by 2 (0 self)
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This paper is concerned with computing viscosity solutions of Hamilton–Jacobi equations using highorder Godunovtype projectionevolution methods. These schemes employ piecewise polynomial reconstructions, and it is a wellknown fact that the use of more compressive limiters or higher
Results 1  10
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21