Periodic parabolic problem with discontinuous coefficients: Mathematical analysis and numerical simulation

This work presents a new approach for the mathematical analysis and numerical simulation of a class of periodic parabolic equations with discontinuous coefficients. Our technique is based on the minimization of a least squares cost function. By the means of variational calculus, we prove that the co...

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Bibliographic Details
Published in:Proyecciones (Antofagasta, Chile) Chile), 2022-10, Vol.41 (6), p.1251-1271
Main Authors: Eddine Alaa, Nour, Charkaoui, Abderrahim, Elaassri, Abdelwahab
Format: Article
Language:English
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Summary:This work presents a new approach for the mathematical analysis and numerical simulation of a class of periodic parabolic equations with discontinuous coefficients. Our technique is based on the minimization of a least squares cost function. By the means of variational calculus, we prove that the considered optimization problem admits an optimal solution. Using the Lagrangian method, we compute the gradient of the cost function associated with our problem. Finally, we give several numerical simulations that show the efficiency and robustness of our method.
ISSN:0717-6279
0717-6279
DOI:10.22199/issn.0717-6279-5017