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

作者：Agnelli J P; Kaufmann U; Rossi J D^*

来源：Journal of Computational and Applied Mathematics, 2018, 342: 133-146.

DOI：10.1016/j.cam.2018.04.016

• Maximal operators
• Numerical approximations
• Obstacle problems

Let Omega subset of R-2 be a polygonal domain, and let L-i, i= 1,2, be two elliptic operators of the form
L(i)u(x) := -div(A(i)(x)Delta u(x) + c(i)(x)u(x) - f(i)(x).
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
{min{L(1)u, L(2)u} = 0 in Omega,
u= 0 on partial derivative Omega.
The convergence of the method is proved, and numerical examples illustrating our results are included.

• 出版日期2018-11