Una implementación computacional del método VEM mixto para el problema de Brinkman en 2d

• SEQUEIRA, FILANDER A. ^[1] ; GUILLÉN OVIEDO, HELEN ^[1]
  1. [1] Universidad Nacional, Escuela de Matemática, Heredia, Costa Rica
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 26, Nº. 2, 2019 (Ejemplar dedicado a: Revista de Matemática: Teoría y Aplicaciones), págs. 215-251
• Idioma: español
• DOI: 10.15517/rmta.v26i2.35968
• Títulos paralelos:
  • A computational implementation of the mixed-VEM method for the brinkman problem in 2d
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• Resumen
  • español

    En este artículo se describen algunos aspectos específicos sobre una implementación computacional para la formulación mixta de elementos virtuales (mixed-VEM, por sus siglas en inglés) del problema lineal de Brinkman en dos dimensiones, con condiciones de frontera de Dirichlet no homogéneas. La formulación empleada fue originalmente propuesta y analizada en CÁCERES, E., GATICA, G.N. AND SEQUEIRA, F.A., A mixed virtual element method for the Brinkman problem. Math. Models Methods Appl. Sci. 27 (2017), no. 4, 707–743. La implementación planteada aquí considera cualquier grado polinomial k >= 0 de manera natural al construir diversas matrices locales de bajo tamaño. Además, se propone un algoritmo para el ensamblaje del sistema lineal global asociado, que garantiza la continuidad de la componente normal en la solución discreta.

  • English

    In this paper we describe some specific aspects on the computational implementation of the a mixed virtual element method (mixed-VEM) for the two-dimensional linear Brinkman model with non-homogeneous Dirichlet boundary conditions. The formulation used below was originally proposed and analysed in CÁCERES, E., GATICA, G.N. AND SEQUEIRA, F.A., A mixed virtual element method for the Brinkman problem. Math. Models Methods Appl. Sci. 27 (2017), no. 4, 707–743. The implementation presented here consider any polynomial degree k >= 0 in a natural way by building several local matrices of small size. In addition, an algorithm is proposed for the assembly of the associated global linear system, which guarantees the continuity of the normal component in the discrete solution.

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