Keywords
finite difference method
unsteady diffusion equation
Lax-Friedrichs equivalence theorem
método mimético
método de diferencias finitas
ecuación no estática de difusión
teorema de equivalencia de Lax-Friedrichs
How to Cite
Abstract
In this article a new mimetic finite difference method to solve unsteady diffusion equation is presented. It uses Crank-Nicolson scheme to obtain time approximations and second order mimetic discretizations for gradient and divergence operators in space. The convergence of this new method is analyzed using Lax-Friedrichs equivalence theorem. This analysis is developed for one dimensional case. In addition to the analytical work, we provide experimental evidences that mimetic Crank-Nicolson scheme is better than standard finite difference because it achieves quadratic conver- gence rates, second order truncation errors and better approximations to the exact solution.
References
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