A mimetic finite difference method using Crank-Nicolson scheme for unsteady diffusion equation
??? n this article a new mimetic finite difference method to solve unsteady diffusionequation is presented. It uses Crank-Nicolson scheme to obtain time approximationsand second order mimetic discretizations for gradient and divergence operators inspace. The convergence of this new method is analyze...
| Main Author: | Mannarino, Iliana A. |
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| Format: | Artículo |
| Language: | Español |
| Published: |
2015
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| Online Access: |
http://revistas.ucr.ac.cr/index.php/matematica/article/view/302 http://hdl.handle.net/10669/12959 |
| Summary: |
??? n this article a new mimetic finite difference method to solve unsteady diffusionequation is presented. It uses Crank-Nicolson scheme to obtain time approximationsand second order mimetic discretizations for gradient and divergence operators inspace. The convergence of this new method is analyzed using Lax-Friedrichs equiv-alence theorem. This analysis is developed for one dimensional case. In addition tothe analytical work, we provide experimental evidences that mimetic Crank-Nicolsonscheme is better than standard finite difference because it achieves quadratic conver-gence rates, second order truncation errors and better approximations to the exactsolution.Keywords: mimetic scheme, finite difference method, unsteady diffusion equation,Lax-Friedrichs equivalence theorem. |
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