BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-77-615
       ENTRY:: June 28, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Numerical methods for the first biharmonic equation and for
               the two-dimensional Stokes problem
        TYPE:: Technical Report
      AUTHOR:: Glowinski, Roland
      AUTHOR:: Pironneau, Olivier
        DATE:: May 1977
       PAGES:: 90
    ABSTRACT:: We describe in this report various methods, iterative and
               "almost direct," for solving the first biharmonic problem on
               general two-dimensional domains once the continuous problem
               has been approximated by an appropriate mixed finite element
               method. Using the approach described in this report we
               recover some well known methods for solving the first
               biharmonic equation as a system of coupled harmonic
               equations, but some of the methods discussed here are
               completely new, including a conjugate gradient type
               algorithm. In the last part of this report we discuss the
               extension of the above methods to the numerical solution of
               the two dimensional Stokes problem in p- connected domains (p
               $\geq$ 1) through the stream function-vorticity formulation.
       NOTES:: [Adminitrivia V1/Prg/19950628]
         END:: STAN//CS-TR-77-615