Algorítmo para la Ecuación de Difusión en Estado Estacionario 2D usando el Método Mimético en Diferencias Finitas.
DOI:
https://doi.org/10.17268/sel.mat.2014.01.04Keywords:
Algoritmo Mimético, Gradiente Mimético, Divergencia Mimética.Abstract
El objetivo principal de este trabajo es la descripción e investigación de un nuevo algoritmo del esquema de diferencias finitas miméticas para resolver la ecuación diferencial parcial elíptica o también conocida como la ecuación estacionaria.
El nuevo algoritmo se formula para una rejilla del cuadrado unitario, el cual nos proporciona
la solución numérica al problema planteado así también como el error de aproximación entre la solución exacta y la aproximada.
Este nuevo algoritmo se deriva usando el esquema de diferencias finitas miméticas, una
idea clave en la obtención de este método, proponer discretizaciones de los operadores
diferenciales fundamentales de la física matemática (divergencia y gradiente), satisfaciendo
o mimetizando el teorema de la divergencia a nivel discreto, la cual es responsable
de cumplir las propiedades conservativas del medio continuo.
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