Discontinuous Galerkin and mimetic finite difference methods for coupled Stokes-Darcy flows on polygonal and polyhedral grids

作者：Lipnikov Konstantin; Vassilev Danail^*; Yotov Ivan

来源：Numerische Mathematik, 2014, 126(2): 321-360.

DOI：10.1007/s00211-013-0563-3

We study locally mass conservative approximations of coupled Darcy and Stokes flows on polygonal and polyhedral meshes. The discontinuous Galerkin (DG) finite element method is used in the Stokes region and the mimetic finite difference method is used in the Darcy region. DG finite element spaces are defined on polygonal and polyhedral grids by introducing lifting operators mapping mimetic degrees of freedom to functional spaces. Optimal convergence estimates for the numerical scheme are derived. Results from computational experiments supporting the theory are presented.

• 出版日期2014-2