Conjugate Gradient-like solution algorithms for the mixed finite element approximation of the biharmonic equation, applied to plate bending problems Original Research Article

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.