Numerical solutions of a two-phase membrane problem (Q610785)

The paper is concerned with a free boundary problem. The right-hand side of the elliptic equation attains different values in the subdomains where the solution \(u\) is positive and where it is negative. A finite element solution is computed iteratively. In each step a linear problem is solved with the right-hand side determined by the sign of the previous approximate solution. A second method uses a regularization at the free boundary.