## Primal discontinuous Galerkin methods for time-dependent coupled surface and subsurface flow.(English)Zbl 1203.76078

Summary: This paper introduces and analyzes a numerical method based on discontinuous finite element methods for solving the two-dimensional coupled problem of time-dependent incompressible Navier-Stokes equations with the Darcy equations through Beaver-Joseph-Saffman’s condition on the interface. The proposed method employs Crank-Nicolson discretization in time (which requires one step of a first order scheme namely backward Euler) and primal DG method in space. With the correct assumption on the first time step optimal error estimates are obtained that are high order in space and second order in time.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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### References:

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