Una Formulación Mixta para el Problema de Poisson Fraccionario
DOI:
https://doi.org/10.70567/mc.v41i15.77Palavras-chave:
Laplaciano fraccionario, formulación mixta, método de elementos finitosResumo
La formulación mixta del problema de Poisson clásico consiste en introducir un flujo como nueva variable con condiciones de borde adecuadas, obteniendo un sistema de ecuaciones acopladas. Usando identidades del cálculo fraccionario, en este trabajo exploramos una formulación mixta del problema de Poisson fraccionario y probamos que el problema está bien planteado. Una discretización directa del problema no es posible, por lo que siguiendo ideas de Hughes y Masud introducimos una formulación estabilizada, que da lugar a un problema coercivo y bien planteado. La coercividad implica que cualquier discretización por elementos finitos conforme sea estable. Por último, obtenemos la convergencia de estas discretizaciones y discutimos su implementación.
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