Ricerc@Sapienza

It has been proved in [10] that the unique viscosity solution of
λuλ +H(x,dxuλ)=c(H) in M (*)
uniformly converges, for λ → 0+, to a specific solution u0 of the critical equation
H(x,dxu) = c(H) in M,

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

The lack of smoothness is a common feature of weak solutions of nonlinear hyperbolic equations and is a crucial issue in their approximation. This has motivated several efforts to define appropriate indicators, based on the values of the approximate solutions, in order to detect the most troublesome regions of the domain. This information helps to adapt the approximation scheme in order to avoid spurious oscillations when using high-order schemes.