Tian, Mingzhong; Chen, Zhongying A generalized difference method for second order elliptic partial differential equations. (Chinese. English summary) Zbl 0734.65083 Numer. Math., Nanjing 13, No. 2, 99-113 (1991). Summary: We present a generalized difference method. The trial subspace is taken as the usual piecewise quadratic finite element space over the triangulation, and the test subspace is defined as the piecewise constant space over the dual subdivision. An optimal rate of convergence is established. Cited in 24 Documents MSC: 65N06 Finite difference methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:second order elliptic partial differential equations; difference method; trial subspace; piecewise quadratic finite element; test subspace; optimal rate of convergence PDFBibTeX XMLCite \textit{M. Tian} and \textit{Z. Chen}, Numer. Math., Nanjing 13, No. 2, 99--113 (1991; Zbl 0734.65083)