Upwind-mixed methods for transport equations

In this paper, we continue our analysis of upwind-mixed methods for advection-diffusion equations, which have been developed and analyzed by the first author over the past several years. In previous work, our analysis has been limited to low order approximating spaces, positive definite diffusion coefficients and Dirichlet boundary conditions. In this paper, we extend our results to higher order approximating spaces, possibly zero diffusion, and more physically realistic boundary conditions. Moreover, unlike previous papers, we avoid the use of Gronwall's Inequality, which can result in extremely large constants in the stability and error bounds. Numerical results are presented for constant, linear and quadratic approximating spaces.