An iterative solver for a mixed variable variational formulation of the (first) biharmonic problem

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The coupled system of equations resulting from a mixed variable formulation of the biharmonic problem is solved by a preconditioned conjugate gradient method. The preconditioning matrix is based on an incomplete factorization of a positive definite operator similar to the 13-point difference approximation of the biharmonic operator. The first iterate is already quite accurate even if the initial approximation is not. Hence, often a small number of iterations will suffice to get an accurate enough solution. For smaller iteration errors the number of iterations grows as O ( h −1), h → 0, where h is an average mesh-size parameter.