Parabolic problem considering diffusion piecewise constant refer to domain using FEM

  • Guillermo Villa Department of Mathematics, Universidad Tecnológica de Pererira, Colombia
  • Carlos Alberto Ramírez Vanegas Department of Mathematics, Universidad Tecnológica de Pererira, Colombia
  • José Rodrigo González Granada Department of Mathematics, Universidad Tecnológica de Pererira, Colombia
DOI: https://doi.org/10.19139/soic-2310-5070-2490
Keywords: finite element method, finite element analysis, partial differential equation, heterogeneous domain, parabolic, piecewise constant, problem, weak formulation, discretization, assembly, reference element, Gaussian quadrature

Abstract

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.
Published
2025-09-18
How to Cite
Villa, G., Vanegas, C. A. R., & Granada, J. R. G. (2025). Parabolic problem considering diffusion piecewise constant refer to domain using FEM. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2490
Issue
Online First
Section
Research Articles
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