Cai, Z.; Lazarov, R.; Manteuffel, T. A.; McCormick, S. F. First-order system least squares for second-order partial differential equations. I. (English) Zbl 0813.65119 SIAM J. Numer. Anal. 31, No. 6, 1785-1799 (1994). Second-order equations are reformulated as a least squares problem for an equivalent first-order system. The ellipticity and convergence of the finite element method are proved. Reviewer: I.Evzerov (Kiev) Cited in 2 ReviewsCited in 144 Documents MSC: 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 equations; least squares problem; first-order system; convergence; finite element method PDFBibTeX XMLCite \textit{Z. Cai} et al., SIAM J. Numer. Anal. 31, No. 6, 1785--1799 (1994; Zbl 0813.65119) Full Text: DOI