Liu, Jinghong; Jia, Yinsuo An estimate for the four-dimensional discrete derivative Green’s function and its applications in FE superconvergence. (English) Zbl 1326.35093 J. Comput. Anal. Appl. 19, No. 3, 462-469 (2015). Summary: In this article we first introduce definitions of the regularized derivative Green’s function, the discrete derivative Green’s function, the discrete derivative \(\delta\) function, and the \(L^2\)-projection operator in four dimensions. Then the \(W^{2,1}\)-seminorm estimates for the regularized derivative Green’s function and the discrete derivative Green’s function are derived. Finally, we show the applications of the \(W^{2,1}\)-seminorm estimate for the discrete derivative Green’s function in finite element (FE) superconvergence. MSC: 35J08 Green’s functions for elliptic equations 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:regularized derivative Green’s function; discrete derivative Green’s function; discrete derivative \(\delta\) function; \(L^2\)-projection operator; \(W^{2,1}\)-seminorm estimate; finite element (FE) superconvergence PDFBibTeX XMLCite \textit{J. Liu} and \textit{Y. Jia}, J. Comput. Anal. Appl. 19, No. 3, 462--469 (2015; Zbl 1326.35093)