The numerical solution of elliptic free boundary problems using multigrid techniques
The article deals with the multigrid V-cycle finite difference method for second order linear elliptic equations with a free part of the boundary. The domain is supposed to allow a smooth mapping on a rectangle with one side corresponding to the free boundary condition. For the numerical solution the problem is rewritten for this rectangle. Nonlinear finite difference equations defined on the given grid and the free boundary are suggested to be solved simultaneously using relaxation along one system of grid lines with a single Newton iteration. Numerical results for three test problems are described.
scientific article; zbMATH DE number 3958660
scientific article