Yang, Dan-Ping Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems. (English) Zbl 0947.65108 Math. Comput. 69, No. 231, 929-963 (2000). Nonlinear nonstationary convection-diffusion problems are discussed, especially from the numerical point of view. A least squares finite element method for solving this nonlinear convection-diffusion problem in a first-order system form is used. A new modified scheme is formulated in the sense of a weighted \(L_2\) norm. A new optimal a priori error estimate in \(L_2\) norm is proved if the classical mixed elements are used. Four fully discrete least squares mixed finite element schemes for the nonlinear first-order system are formulated and systematic theories on convergence of these schemes are established. Reviewer: Angela Handlovičová (Bratislava) Cited in 37 Documents MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35K55 Nonlinear parabolic equations 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 76M10 Finite element methods applied to problems in fluid mechanics 76R05 Forced convection Keywords:nonlinear convection-diffusion problem; least squares algorithm; mixed finite element; convergence; first-order system PDFBibTeX XMLCite \textit{D.-P. Yang}, Math. Comput. 69, No. 231, 929--963 (2000; Zbl 0947.65108) Full Text: DOI References: [1] Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. · Zbl 0314.46030 [2] A. K. 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