Numerical methods for evolutionary problems in partial differential equations and control

  • Guillermo Villa Martínez Department of Mathematics, Universidad Tecnológica de Pererira, Colombia
  • Carlos Alberto Ramírez Vanegas Department of Mathematics, Universidad Tecnológica de Pererira, Colombia
  • Oscar Danilo Montoya Giraldo Grupo de Compatibilidad e interferencia Electromagnética, Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá, 110231, Colombia
DOI: https://doi.org/10.19139/soic-2310-5070-2489
Keywords: finite element method, finite element analysis, partial differential equation, Poission problem, weak formulation, discretization, assembly, reference element, Gaussian quadrature.

Abstract

In this paper we implement the finite element method for parabolic problems with dominant transport terms. The formulation of the linear system of equations coming from a partial differential equation takes its form from the weakening of the problem. Several numerical experiments are performed to know the convergence of the solution and an error analysis in a Sobolev space for linear functions is implemented.
Published
2025-06-23
How to Cite
Martínez , G. V., Ramírez Vanegas, C. A., & Giraldo, O. D. M. (2025). Numerical methods for evolutionary problems in partial differential equations and control. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2489
Issue
Online First
Section
Research Articles
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