<?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>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332025000100014</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v32i1.59472</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A two-level overlapping Schwarz preconditioner for discontinuous Galerkin methods]]></article-title>
<article-title xml:lang="es"><![CDATA[Un precondicionador de Schwarz de dos niveles con traslape para métodos discontinuos de Galerkin]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Calvo]]></surname>
<given-names><![CDATA[Juan G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Solano]]></surname>
<given-names><![CDATA[Moisés]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica Centro de Investigación en Matemática Pura y Aplicada ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Costa Rica Escuela de Matemática ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2025</year>
</pub-date>
<volume>32</volume>
<numero>1</numero>
<fpage>14</fpage>
<lpage>32</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332025000100014&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332025000100014&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332025000100014&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This article introduces a two-level overlapping additive Schwarz algorithm tailored for solving elliptic problems discretized with the symmetric interior penalty discontinuous Galerkin method. The proposed algorithm allows for the use of irregular subdomains, overcoming limitations of other approaches where the coarse mesh was based on triangular elements. Additionally, we provide a brief description of the numerical implementation of the Galerkin method. We present numerical results validating the relevance of our algorithm, including cases where the coefficient of the differential equation is discontinuous-a feature that is particularly relevant to various practical applications.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Este artículo presenta un algoritmo aditivo de Schwarz de dos niveles con traslape diseñado para resolver problemas elípticos discretizados con el método Galerkin discontinuo de penalización interior simétrico. El algoritmo propuesto permite utilizar subdominios irregulares, superando limitaciones de otros enfoques donde la malla gruesa se basaba en elementos triangulares. Se incluye además una breve descripción de la implementación numérica del método de Galerkin. Se presentan resultados numéricos que validan la pertinencia del método, incluyendo casos donde el coeficiente de la ecuación diferencial es discontinuo, una característica que es relevante en diversas aplicaciones.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Domain decomposition]]></kwd>
<kwd lng="en"><![CDATA[Discontinuous Galerkin methods]]></kwd>
<kwd lng="en"><![CDATA[Irregular subdomain boundaries]]></kwd>
<kwd lng="en"><![CDATA[Overlapping Schwarz algorithms]]></kwd>
<kwd lng="en"><![CDATA[Nodal elliptic problems.]]></kwd>
<kwd lng="es"><![CDATA[Descomposición de dominios]]></kwd>
<kwd lng="es"><![CDATA[Métodos discontinuos de Galerkin]]></kwd>
<kwd lng="es"><![CDATA[Subdominios con frontera irregular]]></kwd>
<kwd lng="es"><![CDATA[Algoritmos con traslape de Schwarz]]></kwd>
<kwd lng="es"><![CDATA[Problemas elípticos nodales.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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