A Survey of Trial Free-Boundary Methods for the Numerical Solution of Free Boundary Problems.

A free boundary problem is a (steady-state) boundary value problem involving differential equations on domains parts of whose boundaries, the free boundaries, are unknown and must be determined as part of the solution. A trial free-boundary method is a numerical method for solving free boundary problems in which the boundary is found by guessing the position of the boundary, solving a boundary-value problem in the resulting region, and using this solution to find a new guess for the position of the boundary, the procedure being repeated until the desired accuracy has been attained. This report gives a comprehensive survey of trial free-boundary methods. (Author)