Application of orthogonal collocation on finite elements to a flow problem

The method of orthogonal collocation on finite elements (OCFE) has been used to solve the flow problem of Newtonian fluid in an internally finned tube. Cylindrical coordinates were employed and Legendre shifted orthogonal polynomials were employed as basis functions. An alternating direction implicit (ADI) method was used to solve the resulting set of equations. Better accuracy was achieved by increasing the number of elements for given total interior collocation points. Although, in general, for given total interior collocation points the OCFE method was found marginally superior to the finite difference method in terms of accuracy, the computational time requirement was much higher for the method of orthogonal collocation on finite elements.