Summary.
Interpolation error estimates for a modified 8-node serendipity finite element are derived in both regular and degenerate cases, the latter of which includes the case when the element is of triangular shape. For \(u \in W^{3, p}(K)\) defined over a quadrilateral K, the error for the interpolant \(\Pi_K u\) is estimated as \(|u-\Pi_K u|_{W^{\alpha, p}(K)}\le Ch^{3-\alpha}_K|u|_{W^{3,p}(K)}\) \((\alpha=0, 1)\), where \(1 \le p \le +\infty\) in the regular case and \(1\le p < 3\) in the degenerate case, respectively. Thus, the obtained error estimate in the degenerate case is of the same quality as in the regular case at least for \(1\le p<3\). Results for some related elements are also given.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received June 2, 1997 / Published online March 16, 2000
Rights and permissions
About this article
Cite this article
Zhang, J., Kikuchi, F. Interpolation error estimates of a modified 8-node serendipity finite element. Numer. Math. 85, 503–524 (2000). https://doi.org/10.1007/s002110000104
Issue Date:
DOI: https://doi.org/10.1007/s002110000104