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An estimate for the four-dimensional discrete derivative Green’s function and its applications in FE superconvergence. (English) Zbl 1326.35093

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
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