A posteriori error estimates for fourth-order elliptic problems

We extend the dichotomy principle of Babuska and Yu [Math. Numerica Sinica 13 (1991) 89: Math. Numerica Sinica 13 (1991) 307] and Adjerid et al. [Math. Mod. Meth. Appl. S. 9 (1999) 261; SIAM J. Sci. Comput. 21 (1999) 728] for estimating the finite element discretization error to fourth-order elliptic problems. We show how to construct a posteriori error estimates from jumps of the third partial derivatives of the finite element solution when the finite element space consists of piecewise polynomials of odd-degree and from the interior residuals for even-degree approximations on meshes of square elements. These estimates are shown to converge to the true error under mesh refinement. We also show that these a posteriori error estimates are asymptotically correct for more general finite element spaces. Computational results from several examples show that the error estimates are accurate and efficient on rectangular meshes. (C) 2002 Elsevier Science B.V. All rights reserved.