CONVERGENCE OF MUSCL AND FILTERED SCHEMES FOR SCALAR CONSERVATION-LAWS AND HAMILTON-JACOBI EQUATIONS

This paper considers the questions of convergence of: (i) MUSCL type (i.e. second-order, TVD) finite-difference approximations towards the entropic weak solution of scalar, one-dimensional conservation laws with strictly convex flux and (ii) higher-order schemes (filtered to ''preserve'' an upper-bound on some weak second-order finite differences) towards the viscosity solution of scalar, multi-dimensional Hamilton-Jacobi equations with convex Hamiltonians.