## Unified finite element discretizations of coupled Darcy-Stokes flow.(English)Zbl 1157.76026

Summary: We discuss some new finite element methods for flows which are governed by the linear stationary Stokes system on one part of the domain and by a second order elliptic equation derived from Darcy’s law in the rest of the domain, and where the solutions in the two domains are coupled by proper interface conditions. All the methods proposed here utilize the same finite element spaces on the entire domain. In particular, we show how the coupled problem can be solved by using standard Stokes elements like the MINI element or the Taylor-Hood element in the entire domain. Furthermore, for all the methods the handling of the interface conditions is straightforward.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76S05 Flows in porous media; filtration; seepage 76D07 Stokes and related (Oseen, etc.) flows

### Keywords:

nonconforming finite elements; interface conditions
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### References:

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