Abstract
In this paper, we have, as a primary objective of the study of the solution of the heat equation subject to initial and limit conditions of Dirichlet, applying numerical analysis, in particular the finite element method, to solve a time-dependent partial differential equation due to the non-linearity of this equation and the complexity of the domain. It is intended to observe that the three-dimensional heat conduction given in a set of four bricks with different conductivities has a Gaussian internal heat source, with all faces maintained at zero temperature, but as time passes, the temperature will reach a stable distribution. On the other hand, we expect that the boundary and initial conditions allow imposing different values of the temperature variable both in the contour of each material and in the temporal dynamics allowing reaching the steady state and the attenuation in terms of spatial distribution. We believe that the work that we present below is scientifically new, and innovative given how the problem posed is solved since it increasingly shows the use of this powerful tool such as the finite element method. Keywords: Temporal Dynamics, Spatial Distribution, Heat Equation, Partial Differential Equations, Boundary Conditions DOI： https://doi.org/10.35741/issn.0258-2724.58.1.42
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