<?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>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2022000200169</article-id>
<article-id pub-id-type="doi">10.18273/revint.v40n2-2022003</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Finite di&#64256;erence and finite element methods for partial di&#64256;erential equations on fractals]]></article-title>
<article-title xml:lang="es"><![CDATA[Métodos de diferencias finitas y elementos finitos para ecuaciones diferenciales parciales sobre dominios fractales]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[CONTRERAS H.]]></surname>
<given-names><![CDATA[LUIS F.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[GALVIS]]></surname>
<given-names><![CDATA[JUAN]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia  ]]></institution>
<addr-line><![CDATA[Bogotá D.C]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>40</volume>
<numero>2</numero>
<fpage>169</fpage>
<lpage>190</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2022000200169&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2022000200169&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2022000200169&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. In this paper, we present numerical procedures to compute so-lutions of partial di&#64256;erential equations posed on fractals. In particular, we consider the strong form of the equation using standard graph Laplacian ma-trices and also weak forms of the equation derived using standard length or area measure on a discrete approximation of the fractal set. We then intro-duce a numerical procedure to normalize the obtained di&#64256;usions, that is, a way to compute the renormalization constant needed in the definitions of the actual partial di&#64256;erential equation on the fractal set. A particular case that is studied in detail is the solution of the Dirichlet problem in the Sierpinski triangle. Other examples are also presented including a non-planar Hata tree.  MSC2010:  65N30, 28A80, 35J20, 35J15.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. En este artículo, se presenta un procedimiento numérico para cal-cular la solución de ecuaciones diferenciales parciales planteadas sobre un dominio fractal. En particular, consideramos la forma fuerte de la ecuación diferencial usando matrices Laplacianas y también la forma débil de la ecua-ción usando medidas estándar de longitud o área en una aproximación dis-creta al conjunto fractal. Luego se presenta un procedimiento numérico para normalizar las difusiones que se obtienen, es decir, una forma de calcular la constante de renormalización necesaria en las definiciones de la ecuación dife-rencial parcial real en el conjunto fractal. Un caso particular que se estudia en detalle es la solución del problema de Dirichlet en el triángulo de Sierpinski, también se presentan otros ejemplos, incluido el árbol Hata en el espacio.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Fractal di&#64256;usion]]></kwd>
<kwd lng="en"><![CDATA[Laplacian on a fractal]]></kwd>
<kwd lng="en"><![CDATA[Renormalization con-stant]]></kwd>
<kwd lng="es"><![CDATA[Difusión fractal]]></kwd>
<kwd lng="es"><![CDATA[Laplaciano sobre un fractal]]></kwd>
<kwd lng="es"><![CDATA[constante de renormaliza-ción]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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