Geodesic
An iterative method for mixed finite element schemes
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 4, pp. 5-10

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This article proposes and investigates an iterative method with a saddle preconditioner for solving a system of nonlinear equations that arises in the approximation of a quasilinear second-order elliptic equation with a mixed scheme of finite elements of Raviart–Thomas type. The ways of choosing iteration parameters to ensure convergence of the method are indicated. The results of numerical experiments are presented.
Keywords: second-order quasilinear elliptic equation, mixed finite element method, iterative method, saddle matrix, convergence investigation. 
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     author = {A. P. Gogin and M. M. Karchevsky},
     title = {An iterative method for mixed finite element schemes},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {5--10},
     publisher = {mathdoc},
     volume = {153},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2011_153_4_a0/}
}
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A. P. Gogin; M. M. Karchevsky. An iterative method for mixed finite element schemes. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 4, pp. 5-10. http://geodesic.mathdoc.fr/item/UZKU_2011_153_4_a0/