The integrated singular basis function method for the stick‐slip and the die‐swell problems

Abstract

We further develop a new singular finite element method, the integrated singular basis function method (ISBFM), for the solution of Newtonian flow problems with stress singularities. The ISBFM is based on the direct subtraction of the leading local solution terms from the governing equations and boundary conditions of the original problem, followed by a double integration by parts applied to those integrals with singular contributions. The method is applied to the stick‐slip and the die‐swell problems and improves the accuracy of the numerical results in both cases. In the case of the die‐swell problem it considerably accelerates the convergence of the free surface profile with mesh refinement. The advantages and disadvantages of the ISBFM when compared to other singular methods are also discussed. Copyright © 1991 John Wiley & Sons, Ltd