Accurate approximations to time-dependent nonlinear convection–diffusion problems

摘要

A new technique to improve the accuracy of the spatial discretization of nonlinear convection–diffusion equations is introduced. Both h- and p-versions of the finite-element method are considered. The procedure amounts to solving a discrete stationary convection–diffusion problem with data based on the computed standard Galerkin approximation at any fixed time. We prove that the convergence rate is increased. Numerical experiments confirm the increase in the convergence rate and show that the procedure we propose annihilates the oscillations of the Galerkin approximation in the convection-dominated regime.