Let Ω⊂ℝ2 be open, bounded and convex. The solution of the biharmonic equa — tion is constructed using the orthogonal projector P from L2 (Ω) onto the subspace X of harmonic functions in ft. For a rectangular domain Ω, the projector P can be given explicitly by the decomposition of X as in the paper of ARONSZAJN — BROWN — BUTCHER [3] . Using tensor products one can carry over this construction to domains which consist of the cartesian product of circles, ellipses, and rectangles. With the partial sums of the series, that represents P, one can give approximate solutions to the exact solution of the biharmonic equation. A combination of this method and the finite element method leads to approximate solutions of O(h2) convergence in the Sobolev space W 2 2


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© Springer Basel AG 1979

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  • Ulrich Tippenhauer

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