A family of rectangular mixed elements with a continuous flux for second order elliptic problems.

*(English)*Zbl 1081.65106Standard mixed finite elements for second order elliptic problems make use of the flux in $H\left(div\right)$. The authors indicate two examples of applied problems for which it is desirable to have continuous approximations for the flux (simulation of fluid flow in a porous medium and the coupling of Stokes and Darcy flows). The authors present a family of mixed elements with continuous flux on rectangular grids and their generalization for three-dimensinal case. A suboptimal convergence is proved and numerical experiments are presented in the end of the paper.

It should be noted that some notation is not specifed at the proper time (see page 1915, for example).

Reviewer: Evgenij D’yakonov (Moskva)

##### MSC:

65N30 | Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) |

65N15 | Error bounds (BVP of PDE) |

35J25 | Second order elliptic equations, boundary value problems |

76M10 | Finite element methods (fluid mechanics) |

76D07 | Stokes and related (Oseen, etc.) flows |

76S05 | Flows in porous media; filtration; seepage |

35Q30 | Stokes and Navier-Stokes equations |