The use of a Legendre pseudospectral viscosity technique to solve a class of nonlinear dynamic HamiltonJacobi equations
In this research, we study the problem of finding the approximate solution of a class of HamiltonJacobi 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.
hamiltonjacobi equations eikonal equation pseudospectral viscosity method legendre polynomials level set method