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A family of rectangular mixed elements with a continuous flux for second order elliptic problems. (English) Zbl 1081.65106
Standard mixed finite elements for second order elliptic problems make use of the flux in $H(div)$. 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).

##### 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
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