Periodic parabolic problem with discontinuous coefficients: Mathematical analysis and numerical simulation
Nour Eddine Alaa, Abderrahim Charkaoui, Abdelwahab Elaassri · Proyecciones (Antofagasta) · 2022
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.