• Article  

      An efficient finite element method for treating singularities in Laplace's equation 

      Olson, L. G.; Georgiou, Georgios C.; Schultz, W. W. (1991)
      We present a new finite element method for solving partial differential equations with singularities caused by abrupt changes in boundary conditions or sudden changes in boundary shape. Terms from the local solution ...
    • Article  

      A singular finite element for Stokes flow: The stick–slip problem 

      Georgiou, Georgios C.; Olson, L. G.; Schultz, W. W.; Sagan, S. (1989)
      Abrupt changes in boundary conditions in viscous flow problems give rise to stress singularities. Ordinary finite element methods account effectively for the global solution but perform poorly near the singularity. In this ...
    • Article  

      Singular finite elements for the sudden‐expansion and the die‐swell problems 

      Georgiou, Georgios C.; Schultz, W. W.; Olson, L. G. (1990)
      The singular finite element method is used to solve the sudden‐expansion and the die‐swell problems in order to improve the accuracy of the solution in the vicinity of the singularity and to speed up the convergence. The ...
    • Conference Object  

      Steady flow of a two-dimensional film under pressure 

      Georgiou, Georgios C.; Tsamopoulos, J.; Schultz, W. W. (2000)
      We use finite elements and the full Newton iteration method to solve the steady, two-dimensional flow of a Newtonian planar film, issuing from a slit under a pressure difference between the two free surfaces, in the presence ...