The w‐plane finite element method for the solution of scalar field problems in two dimensions

A simple, efficient finite element method has been presented for the solution of a variety of scalar field problems in two dimensions. It is based on the mapping of the physical problem domain into an ‘image’ domain in the w-plane. The governing equation(s) and the boundary conditions in the physical plane are also appropriately transformed into the w-plane. The processes of standard finite element analysis are then implemented to obtain a solution in the w-plane. The method has been explained in detail, with illustrative examples where appropriate; it has several important advantages over the standard finite element method, particularly for the solution of infinite or semi-infinite domain problems. The method has been demonstrated to be simple, efficient, economical and potentially capable of dealing with a large repartoire of two-dimensional problems, including non-homogeneity, nonlinearity, etc.