Convergence analysis of least-squares mixed finite elements
The paper deals with theoretical error estimates for the least squares finite element method applied to a system of first order ordinary differential equations. The estimates are consistent with the numerical studies of \textit{G. F. Carey} and \textit{Y. Shen} [Commun. Appl. Numer. Methods 5, No. 7, 427-434 (1989; Zbl 0684.65083)] for the same system. It is proved that the least squares method is not subject to the Ladyzhenskaya-Babuska-Brezzi condition. Some questions are still to be resolved and it is also indicated that the results may be extended to higher dimensions.
system of first order ordinary differential equations
scientific article; zbMATH DE number 482256
scientific article