An Optimal-Order Error Estimate for a Finite Difference Method to Transient Degenerate Advection-Diffusion Equations
Year: 2012
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 1 : pp. 56–72
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-611
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 1 : pp. 56–72
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Convergence analysis degenerate advection-diffusion equations finite difference methods optimal-order error estimates.