Método de los elementos finitos para determinar las cargas hidráulicas en un sistema de acuífero costero
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Date
2025
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Universidad Nacional de Trujillo
Abstract
En este trabajo se hace un estudio para derivar la solución numérica de un problema
de Cauchy-Dirichlet utilizando el método de los elementos finitos, interpretado como
un problema que determina los niveles piezométricos donde una de las fronteras del
dominio lo podemos entender como el flujo de marea. Se realizó la formulación variacional del problema de Cauchy-Dirichlet y se utilizó el método de Faedo de Galerkin
para determinar la existencia y unicidad de la solución débil del problema variacional.
Para la solución numérica se empleó el método de los elementos finitos con elementos
triangulares lineales, además de usar el método de Galerkin en cada nivel de tiempo,
el cual origina un sistema de ecuaciones diferenciales. Finalmente se desarrolló un programa computacional para hallar la solución numérica del problema Cauchy- Dirichlet
en un dominio de geometría irregular.
In this work, a study is carried out to derive the numerical solution of a problem of Cauchy-Dirichlet using the finite element method, interpreted as a problem that determines the piezometric levels where one of the boundaries of the domain defines it. we can understand as the tidal flow. The variational formulation of the problem was carried out Cauchy-Dirichlet and Galerkin’s Faedo method was used to determine the existence and uniqueness of the weak solution of the variational problem. For the numerical solution The finite element method was used with linear triangular elements, in addition to use Galerkin’s method at each time level, which generates a system of equations differentials. Finally, a computer program was developed to find the solution. Numerical Cauchy-Dirichlet problem in an irregular geometry domain.
In this work, a study is carried out to derive the numerical solution of a problem of Cauchy-Dirichlet using the finite element method, interpreted as a problem that determines the piezometric levels where one of the boundaries of the domain defines it. we can understand as the tidal flow. The variational formulation of the problem was carried out Cauchy-Dirichlet and Galerkin’s Faedo method was used to determine the existence and uniqueness of the weak solution of the variational problem. For the numerical solution The finite element method was used with linear triangular elements, in addition to use Galerkin’s method at each time level, which generates a system of equations differentials. Finally, a computer program was developed to find the solution. Numerical Cauchy-Dirichlet problem in an irregular geometry domain.
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Keywords
Cauchy-Dirichlet, Faedo Galerkin, Galerkin, Elemento finito, Diferencias finitas