Introducción físico matemática del Método del Elemento Finito
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Differential equations with partial derivatives are critical for the development of mathematical analysis and for modeling a variety of situations involving chemical, biological, astronomical, and geological phenomena, to name a few. Certain physical phenomena are described by partial derivative equations whose solutions pose difficulties at the analytical level or simply do not exist. After that, non-analytical techniques such as graphical methods, experimental methods, analogical methods, and numerical methods are used. In the present work, numerical methods will be used. These methods have gained prominence in solving a wide variety of problems in Physics and Engineering as a result of the development of fast digital computers. The finite difference and finite element methods are two of the most frequently used numerical techniques in physics and engineering. In the finite difference method, the solution region is represented by a network of grid points. This limits its regular application to border issues. This restriction does not apply to the finite element method because it deals with irregular shapes, handles an infinite number of boundary conditions, and varies the size of the elements to allow for the use of small elements where necessary. The purpose of this work is to provide an overview of the Finite Element Method (FEM) for numerically solving differential equations in partial derivatives that describe physical phenomena and to develop the method by explaining each stage so that the user can implement it computationally.