A comparison of scalar singular finite elements applied to the analysis of homogeneous waveguides with sharp edges

Abstract

When we solve the wave equation by the finite element method, the order of convergence and the accuracy of the solution are reduced by the presence of sharp edges. The employment of singular elements improves the solution and allows us to reduce the cost of computation. In this paper, three types of scalar singular finite elements with the capacity to handle singularities in the derivative, and which have previously been applied to mechanical problems, are examined, together with standard elements, in the context of homogeneous waveguide analysis. We solve two examples of homogeneous waveguides showing the different behaviour of the singular elements and obtaining information on the order of convergence and the approximation of the gradient of the unknown function. © 1997 John Wiley & Sons, Ltd.