An iterative method for the solution of some semilinear elliptic systems with discontinuities (Q1343726)

The authors present a general iterative method which can be used, in particular, to find solutions of a kind of semilinear elliptic system with discontinuities. The algorithm is obtained by adapting some ideas which have been previously introduced by \textit{C. Moreno} and the second author [Math. Comput. 50, No. 181, 139-153 (1988; Zbl 0636.65058)] in the framework of a single equation. More precisely, it relies on fixed-point reformulation and exact regularization. A convergence result is proved under quite general assumptions.