An optimal-order error estimate for a finite diffusion method to transient degenerate advection-diffusion equations
T. Lu 1, J. Jia 11 School of Mathematics, Shandong University, Jinan, Shandong 250100, China
Received by the editors August 18, 2009 and, in revised form, December 21, 2009.
We prove an optimal-order error estimate in a degenerate-diffusion weighted energy norm for implicit Euler and Crank-Nicolson finite difference methods to two-dimensional time-dependent advection-diffusion equations with degenerate diffusion. In the estimate, the generic constants depend only on certain Sobolev norms of the true solution but not on the lower bound of the diffusion. This estimate, combined with a known stability estimate of the true solution of the governing partial differential equations, yields an optimal-order estimate of the finite difference methods, in which the generic constants depend only on the Sobolev norms of the initial and right-hand side data.AMS subject classifications: 65N06, 65N15
Key words: Convergence analysis, degenerate advection-diffusion equations, finite difference methods, optimal-order error estimates.