Parabolic problem considering diffusion piecewise constant refer to domain using FEM

Authors

  • 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.

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Published

2025-09-18

Issue

Vol. 14 No. 6 (2025)

Section

Research Articles

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How to Cite

Parabolic problem considering diffusion piecewise constant refer to domain using FEM. (2025). Statistics, Optimization & Information Computing, 14(6), 3651-3666. https://doi.org/10.19139/soic-2310-5070-2490