<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>2215-3470</journal-id>
<journal-title><![CDATA[Uniciencia]]></journal-title>
<abbrev-journal-title><![CDATA[Uniciencia]]></abbrev-journal-title>
<issn>2215-3470</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional, Costa Rica]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2215-34702020000200055</article-id>
<article-id pub-id-type="doi">10.15359/ru.34-2.4</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Description and implementation of an algebraic multigrid preconditioner for H1-conforming finite element schemes]]></article-title>
<article-title xml:lang="es"><![CDATA[Descripción e implementación de un precondicionador multinivel algebraico para esquemas de elementos finitos H1-conformes]]></article-title>
<article-title xml:lang="pt"><![CDATA[Descrição e implementação de um pré-condicionador multinível algébrico para esquemas de elementos finitos H1-conformes]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Guillén-Oviedo]]></surname>
<given-names><![CDATA[Helen]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ramírez-Jiménez]]></surname>
<given-names><![CDATA[Jeremías]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Segura-Ugalde]]></surname>
<given-names><![CDATA[Esteban]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sequeira-Chavarría]]></surname>
<given-names><![CDATA[Filánder]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Escuela de Matemática ]]></institution>
<addr-line><![CDATA[Heredia ]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,aff2  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Costa Rica Escuela de Matemática Centro de Investigación en Matemática Pura y Aplicada]]></institution>
<addr-line><![CDATA[San José ]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad Nacional Escuela de Matemática ]]></institution>
<addr-line><![CDATA[Heredia ]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<volume>34</volume>
<numero>2</numero>
<fpage>55</fpage>
<lpage>81</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702020000200055&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702020000200055&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702020000200055&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This paper presents detailed aspects regarding the implementation of the Finite Element Method (FEM) to solve a Poisson&#8217;s equation with homogeneous boundary conditions. The aim of this paper is to clarify details of this implementation, such as the construction of algorithms, implementation of numerical experiments, and their results. For such purpose, the continuous problem is described, and a classical FEM approach is used to solve it. In addition, a multilevel technique is implemented for an efficient resolution of the corresponding linear system, describing and including some diagrams to explain the process and presenting the implementation codes in MATLAB®. Finally, codes are validated using several numerical experiments. Results show an adequate behavior of the preconditioner since the number of iterations of the PCG method does not increase, even when the mesh size is reduced.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este artículo se presenta, en forma detallada, aspectos sobre la implementación del Método de Elementos Finitos (FEM, por sus siglas en inglés), para resolver una ecuación de Poisson con condiciones de frontera homogéneas. El objetivo de este trabajo es clarificar los detalles de esta implementación, tales como la construcción de los algoritmos, creación de experimentos numéricos y los resultados acerca de estos. Por ello, se describe el problema continuo y se muestra un enfoque FEM clásico para resolverlo. Después, se establece una técnica multiniveles para la resolución eficiente del sistema lineal correspondiente, que describe e incluye algunos diagramas para explicar el proceso y presenta los códigos de la implementación en MATLAB®. Finalmente, se realiza una validación de los códigos con varios experimentos numéricos. Los resultados muestran un comportamiento adecuado del precondicionador debido a que el número de iteraciones del método PCG no se incrementa, incluso cuando el tamaño de la malla se reduce.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[ Resumo Este artigo apresenta, em detalhes, aspectos sobre a implementação do Método dos Elementos Finitos (MEF) para resolver uma equação de Poisson com condições de contorno homogêneas. O objetivo deste trabalho é esclarecer os detalhes dessa implementação, tais como a construção dos algoritmos, a criação de experimentos numéricos e os resultados sobre eles. Descreve-se, portanto, o problema contínuo e mostra-se uma abordagem clássica do MEF para resolvê-lo. Em seguida, estabelece-se uma técnica multinível para a resolução eficiente do sistema linear correspondente, que descreve e inclui alguns diagramas para explicar o processo e apresenta os códigos de implementação no MATLAB®. Finalmente, realiza-se uma validação dos códigos com várias experiências numéricas. Os resultados mostram um comportamento adequado do pré-condicionador devido ao número de iterações do método PCG não aumentar, mesmo quando o tamanho da malha é reduzido.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Finite element methods]]></kwd>
<kwd lng="en"><![CDATA[H1-conforming schemes]]></kwd>
<kwd lng="en"><![CDATA[low-order approximations]]></kwd>
<kwd lng="en"><![CDATA[multilevel techniques]]></kwd>
<kwd lng="en"><![CDATA[computational implementation]]></kwd>
<kwd lng="en"><![CDATA[MATLAB®]]></kwd>
<kwd lng="es"><![CDATA[Métodos de elementos finitos]]></kwd>
<kwd lng="es"><![CDATA[esquemas H1 conformes]]></kwd>
<kwd lng="es"><![CDATA[aproximaciones de bajo orden]]></kwd>
<kwd lng="es"><![CDATA[técnicas multiniveles]]></kwd>
<kwd lng="es"><![CDATA[implementación computacional]]></kwd>
<kwd lng="es"><![CDATA[MATLAB®]]></kwd>
<kwd lng="pt"><![CDATA[Métodos de elementos finitos]]></kwd>
<kwd lng="pt"><![CDATA[esquemas H1 compatíveis]]></kwd>
<kwd lng="pt"><![CDATA[aproximações de baixa ordem]]></kwd>
<kwd lng="pt"><![CDATA[técnicas multiníveis]]></kwd>
<kwd lng="pt"><![CDATA[implementação computacional]]></kwd>
<kwd lng="pt"><![CDATA[MATLAB®]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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