Fixed mesh finite element approximations to a free boundary problem for an elliptic equation with an oblique derivative boundary condition (Q1075028)

The approximate solution of an elliptic equation with an oblique derivative on a curved boundary using an unfitted finite element mesh is presented and discussed. The order of accuracy of the fitted mesh finite element method is preserved. A similar result is obtained for a variational inequality. The approach is used to approximate the solution of a free boundary problem on a fixed mesh.