Numerical approximation of equations involving minimal/maximal operators by successive solution of obstacle problems

Let Ω⊂R2 be a polygonal domain, and let Li, i=1,2, be two elliptic operators of the form Liu(x):=−div(Aix∇u(x))+cixu(x)−fix.Motivated by the results in Blanc et al. (2016), we propose a numerical iterative method to compute the numerical approximation to the solution of the minimal problem minL1u,L2u=0in Ω,u=0on ∂Ω.The convergence of the method is proved, and numerical examples illustrating our results are included.