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Revista de Matemática Teoría y Aplicaciones

versión impresa ISSN 1409-2433

Rev. Mat vol.26 no.2 San José jul./dic. 2019

http://dx.doi.org/10.15517/rmta.v26i2.35968 

Artículo

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

A computational implementation of the mixed-VEM method for the Brinkman problem in 2d

Helen Guillén-Oviedo1 

Filánder A. Sequeira2 

1Universidad Nacional, Escuela de Matemática, Heredia, Costa Rica.hellen.guillen.oviedo@una.ac.cr

2Universidad Nacional, Escuela de Matemática, Heredia, Costa Rica. filander.sequeira.chavarria@una.ac.cr

Resumen

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 [18]. 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.

Palabras clave: modelo de Brinkman; método mixto de elementos virtuales; aproximaciones de alto orden; implementación computacional

Abstract

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 [18]. 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.

Keywords: Brinkman model; mixed virtual element method; high-order approximations; computational implementation

Mathematics Subject Classification: 65N30, 65K05

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Agradecimientos

Este trabajo fue financiado por la Universidad Nacional, a través del proyecto 0106-16

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Recibido: 19 de Febrero de 2019; Revisado: 09 de Mayo de 2019; Aprobado: 23 de Mayo de 2019

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