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Parabolic problem considering diffusion piecewise constant refer to domain using FEM

Year: 2025

Type: article

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.

Source: Statistics Optimization & Information Computing

DOI: 10.19139/soic-2310-5070-2490

Authors: Guillermo Villa, Carlos Alberto Ramírez Vanegas, José Rodrigo González Granada

Institution: Technological University of Pereira

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funder: Universidad Tecnológica de Pereira

OpenAlex ID: W4416895015

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