2026-04-28T20:47:06Zhttps://riubu.ubu.es/oai/request

oai:riubu.ubu.es:10259/80792024-10-05T22:42:07Zcom_10259_6229com_10259_4534com_10259.4_106com_10259_2604col_10259_6230

Serna-Reyes, Adán 69c1a9ba-b3da-4512-ae09-98a5ce446551 600 Macías Díaz, Jorge E. d15a1e35-0c8a-4334-9c9e-0ded4276cfa3 600 Reguera López, Nuria 470 600 0000-0002-6219-5531 2023-11-21T12:39:44Z 2023-11-21T12:39:44Z 2023-01 0168-9274 http://hdl.handle.net/10259/8079 10.1016/j.apnum.2022.09.015 Get rights and content 1873-5460 In this work, we design and analyze a discrete model to approximate the solutions of a parabolic partial differential equation in multiple dimensions. The mathematical model considers a nonlinear reaction term and a space-dependent diffusion coefficient. The system has a Gibbs' free energy, we establish rigorously that it is non-negative under suitable conditions, and that it is dissipated with respect to time. The discrete model proposed in this work has also a discrete form of the Gibbs' free energy. Using a fixed-point theorem, we prove the existence of solutions for the numerical model under suitable assumptions on the regularity of the component functions. We prove that the scheme preserves the positivity and the dissipation of the discrete Gibbs' free energy. We establish theoretically that the discrete model is a second-order consistent scheme. We prove the stability of the method along with its quadratic convergence. Some simulations illustrating the capability of the scheme to preserve the dissipation of Gibb's energy are presented. The corresponding author (J.E.M.-D.) wishes to acknowledge the financial support from the National Council for Science and Technology of Mexico (CONACYT) through grant A1-S-45928. application/pdf eng Elsevier Applied Numerical Mathematics. 2023, V. 183, p. 355-368 https://doi.org/10.1016/j.apnum.2022.09.015 info:eu-repo/grantAgreement/CONACYT//A1-S-45928/MX/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Nonlinear diffusion-reaction equation Dissipation of Gibbs' free energy Structure-preserving numerical model Stability and convergence analysis Matemáticas Mathematics Analysis of a scheme which preserves the dissipation and positivity of Gibbs' energy for a nonlinear parabolic equation with variable diffusion info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion THUMBNAIL Serna-anm_2023.pdf.jpg Serna-anm_2023.pdf.jpg IM Thumbnail image/jpeg 4192 https://riubu.ubu.es/bitstream/10259/8079/4/Serna-anm_2023.pdf.jpg 57f5cf1ce1c90697e80c86578496b721 MD5 4 LICENSE license.txt license.txt text/plain; charset=utf-8 999 https://riubu.ubu.es/bitstream/10259/8079/3/license.txt b295bcbce42e2caabeb0c623d3860c06 MD5 3 CC-LICENSE license_rdf license_rdf application/rdf+xml; charset=utf-8 805 https://riubu.ubu.es/bitstream/10259/8079/2/license_rdf 4460e5956bc1d1639be9ae6146a50347 MD5 2 ORIGINAL Serna-anm_2023.pdf Serna-anm_2023.pdf application/pdf 686367 https://riubu.ubu.es/bitstream/10259/8079/1/Serna-anm_2023.pdf b747b6e69c7a7b0a1c8f3ea77f71a182 MD5 1 10259/8079 oai:riubu.ubu.es:10259/8079 2024-10-06 00:42:07.42 Repositorio Institucional de la Universidad de Burgos bubrep@ubu.es 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