FIXED MESH FINITE ELEMENT APPROXIMATIONS TO A FREE BOUNDARY PROBLEM FOR AN ELLIPTIC EQUATION WITH AN OBLIQUE DERIVATIVE BOUNDARY CONDITION

A method for approximating the solution of an elliptic equation with an oblique derivative on a curved boundary using an unfitted finite element mesh is presented and analysed. It is shown that the method retains the order of accuracy of the fitted mesh finite element method. A similar result is obtained for a variational inequality. The usefulness of this approach is then demonstrated by using it to approximate the solution of a free boundary problem on a fixed mesh.