Sharp error estimates for a discretisation of the 1D convection/diffusion equation with Dirac initial data

This paper derives sharp l∞ and l1 estimates of the error arising from an explicit approximation of the constant coefficient 1D convection/diffusion equation with Dirac initial data. The analysis embeds the discrete equations within a semi-discrete system of equations which can be solved by Fourier analysis. The error estimates are then obtained though asymptotic approximation of the integrals resulting from the inverse Fourier transform. This research is motivated by the desire to prove convergence of approximations to adjoint partial differential equations.