Inverse finite element method for directly formulated free and moving boundary problems

Abstract

In free boundary problems a priori unknown geometric parameters need to be evaluated simultaneously with the primary field unknowns. These problems are highly nonlinear and difficult to handle computationally. Here an accurate and efficient method is presented which can appropriately handle the complexities associated with these problems. The method is based on a tesselation that is constructed by isolines as characteristic coordinates lines. Thus opposite sides of finite elements lie on isolines. The method allows the simultaneous determination of the location of the isolines with the primary unknowns. Its accuracy and efficiency is demonstrated in a number of model problems.