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

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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2018 vol. 342 p. 133 - 146

0377-0427

Let Ω⊂R² be a polygonal domain, and let L_{i}, i=1,2, be two elliptic operators of the formL_{i}u(x):=-div(A_{i}(x)∇u(x))+c_{i}(x)u(x)-f_{i}(x).Motivated by the results in [2], we propose a numerical iterative method to compute the numerical approximation to the solution of the minimal problemmin{L₁u,L₂u}=0in Ω,u=0on ∂Ω.The convergence of the method is proved, and numerical examples illustrating our results are included.