Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions.
WENO-Z scheme with new nonlinear weights for Hamilton-Jacobi equations and adaptive approximation
A new fifth-order weighted essentially nonoscillatory (WENO) scheme is designed to approximate Hamilton-Jacobi equations. As employing a fifth-order linear approximation and three third-order ones on the same six-point stencil as before, a newly considered WENO-Z methodology is adapted to define nonlinear weights and the final WENO reconstruction results in a simple and clear convex combination. The scheme has formal fifth-order accuracy in smooth regions of the solution and nonoscillating behavior...