Rectangular Finite Element for Field Problems

A rectangular finite element suitable for the solution of a class of field problems is presented. The approximating functions satisfy the governing partial differential equation within each element, and are a combination of a polynomial and four trigonometric series, known in terms of nodal values and trigonometric series coefficients on the edges of the element. The degrees-of-freedom of the element may be readily varied to give an indication of convergence to the exact solution. As the governing equation is satisfied within each element, large elements, sometimes semi-infinite may be used. Two examples are considered, indicating that in those problems where this element can be used, engineering accuracy can be obtained with the solution of fewer equations than with other numerical methods.