Numerical solutions to minimal/maximal operators iterating obstacle problems

ROSSI J.D.; AGNELLI J.P.; KAUFMANN U.

Córdoba

Workshop; Workshop en Ecuaciones en Derivadas Parciales y Aplicaciones; 2017

Centro de Investigación y Estudios de Matemática (CIEM-CONICET)

Let $\Omega$ be a convex polygonal or polyhedral($d=3$) domain, and let $L_{i}$, $i=1,2$, be two elliptic operators of theform: L_{i}u (x):=-\div (A_{i}(x) \nabla u (x))+c_{i}(x) u(x) - f_{i}(x)  We propose a numerical iterative method to compute the numerical solution of the minimal problem:min {L_{1}u, L_{2}u}  = 0  in \Omega,u=0  on  \partial\Omega.The convergence of the method is proved, and numerical examples illustrating our results are included.