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...

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Main Author: Mannarino, Iliana A.
Format: Artículo
Language: Español
Published: 2015
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.