Ricerc@Sapienza

In this paper we consider a class of “filtered” schemes for some first order time dependent Hamilton-Jacobi equations. A typical feature of a filtered scheme is that at the node xj the scheme is obtained as a mixture of a high-order scheme and a

We consider a class of “filtered” schemes for first order time dependent Hamilton–Jacobi equations and prove a general convergence result for this class of schemes. A typical filtered scheme is obtained mixing a high-order scheme and a monotone scheme according to a filter function F which decides where the scheme has to switch from one scheme to the other. A crucial role for this switch is played by a parameter ε= ε(Δ t, Δ x) > 0 which goes to 0 as the time and space steps (Δ t, Δ x) are going to 0 and does not depend on the time tn, for each iteration n.