Convergence of linearized and adjoint approximations for discontinuous solutions of conservation laws. Part 1: linearized approximations and linearized output functionals

This paper analyzes the convergence of discrete approximations to the linearized equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. A simple modified Lax–Friedrichs discretization is used on a uniform grid, and a key point is that the numerical smoot...