Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Convergence of spectral methods for nonlinear conservation laws
SIAM Journal on Numerical Analysis
Shock capturing by the spectral viscosity method
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Legendre pseudospectral viscosity method for nonlinear conservation laws
SIAM Journal on Numerical Analysis
A level set formulation for the solution of the Dirichlet problem for Hamilton-Jacobi equations
SIAM Journal on Mathematical Analysis
The spectral viscosity method applied to simulation of waves in a stratified atmosphere
Journal of Computational Physics
A fast level set method for propagating interfaces
Journal of Computational Physics
A Legendre pseudospectral viscosity method
Journal of Computational Physics
Multi-phase computations in geometrical optics
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
On the Gibbs Phenomenon and Its Resolution
SIAM Review
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
A PDE-based fast local level set method
Journal of Computational Physics
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
A spectral vanishing viscosity method for large-eddy simulations
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Optimal Algorithm for Shape from Shading and Path Planning
Journal of Mathematical Imaging and Vision
SIAM Journal on Numerical Analysis
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Spectral Viscosity Approximations to Hamilton--Jacobi Solutions
SIAM Journal on Numerical Analysis
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
A spectral viscosity method for correcting the long-term behavior of POD models
Journal of Computational Physics
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
Fast Sweeping Methods for Static Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Mathematics and Computers in Simulation
High Order Fast Sweeping Methods for Static Hamilton---Jacobi Equations
Journal of Scientific Computing
Idempotent filtering in spectral and spectral element methods
Journal of Computational Physics
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
Redistancing by flow of time dependent eikonal equation
Journal of Computational Physics
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
A Fast Iterative Method for Eikonal Equations
SIAM Journal on Scientific Computing
Mathematics and Computers in Simulation
SIAM Journal on Numerical Analysis
A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations
Applied Numerical Mathematics
Mathematical and Computer Modelling: An International Journal
IEEE Transactions on Image Processing
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In this research, we study the problem of finding the approximate solution of a class of Hamilton-Jacobi equations, namely the Eikonal equation. We employ the Legendre pseudospectral viscosity method to solve this problem. This method basically consists of adding a spectral viscosity to the equation. This spectral viscosity, which is sufficiently small to retain the formal spectral accuracy is large enough to stabilize the numerical scheme. Several test problems are considered and the numerical results are given to show the efficiency of the proposed method.