A posteriori error estimates for fourth-order elliptic problems Original Research Article

We extend the dichotomy principle of Babuška 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.