CONJUGATE GRADIENT-LIKE SOLUTION ALGORITHMS FOR THE MIXED FINITE-ELEMENT APPROXIMATION OF THE BIHARMONIC EQUATION, APPLIED TO PLATE-BENDING PROBLEMS

Discretization of the Biharmonic Equation with the Mixed Finite Element Method yields an indefinite linear system of equations with a special structure. In this paper two variants of the Conjugate Gradient method are formulated that are suited for solving such systems. They both require the solution of a system of linear equations in every iteration. Different strategies for doing this are examined. An Incomplete Choleski decomposition is used as a preconditioner. Both iterative methods and the preconditioner are chosen so that optimal use can be made of the special block structure of the global system of equations.