- Journal Home
- Volume 22 - 2025
- Volume 21 - 2024
- Volume 20 - 2023
- Volume 19 - 2022
- Volume 18 - 2021
- Volume 17 - 2020
- Volume 16 - 2019
- Volume 15 - 2018
- Volume 14 - 2017
- Volume 13 - 2016
- Volume 12 - 2015
- Volume 11 - 2014
- Volume 10 - 2013
- Volume 9 - 2012
- Volume 8 - 2011
- Volume 7 - 2010
- Volume 6 - 2009
- Volume 5 - 2008
- Volume 4 - 2007
- Volume 3 - 2006
- Volume 2 - 2005
- Volume 1 - 2004
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/611.html} }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.