Parabolic problem considering diffusion piecewise constant refer to domain using FEM - Guillermo Villa; Carlos Alberto Ramírez Vanegas; José Rodrigo González Granada (Statistics, Optimization & Information Computing, 2025)
This paper presents a numerical solution of the one-dimensional heat equation using the Finite Element Method (FEM) with time discretization through the implicit Euler scheme. The formulation considers piecewise constant diffusion coefficients over the spatial domain and employs a weak formulation approach for numerical approximation. The study provides a detailed analysis of the assembly process, including mass, stiffness, and load matrices. Numerical results illustrate the accuracy and stability of the proposed method under different initial conditions and diffusion parameters.