Author(s)

G. Mejak

Abstract

A model free boundary value problem is recasted into the minimization problem which is discretized using the finite element method. The problem is approached by the quasi-Newt on method with the BFGS update of Hessian. Here the gradient of the cost function is computed analytically by solving the adjoint problem. Numerical results are given for various mesh discretizations and four different triangular elements. 1 Introduction A common feature of elliptical free boundary problems (FBVPs) is the presence of an additional condition which together with a governing equa- tion and corresponding boundary conditions determines unknown part of the boundary. As a rule, the governing equation together with the bound- ary conditions constitute a well posed boundary value prob

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