Parabolic problem considering diffusion piecewise constant refer to domain using FEM - Villa, Guillermo; Vanegas, Carlos Alberto Ramírez; Granada, José Rodrigo González (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.