The piecewise parabolic finite analytic method. I: Theory (Q1208762)

The authors consider a numerical scheme (the piecewise parabolic finite analytic method, which they describe) to approximate solutions of convection diffusion equation. This method satisfies a discrete maximum principle analogous to the one satisfied by the continuous equation. The authors obtain existence and uniqueness results for the approximate problem, discuss stability and convergence of the numerical scheme, and derive error estimates using the discrete maximum principle.