Coupling Stokes--Darcy Flow with Transport

A mathematical and numerical model describing chemical transport in a Stokes– Darcy flow system is discussed. The flow equations are solved through domain decomposition using classical finite element methods in the Stokes region and mixed finite element methods in the Darcy region. The local discontinuous Galerkin (LDG) method is used to solve the transport equation. Models dealing with coupling between Stokes and Darcy equations have been extensively discussed in the literature. This paper focuses on the approximation of the transport equation. Stability of the LDG scheme is analyzed, and an a priori error estimate is proved. Several numerical examples verifying the theory and illustrating the capabilities of the method are presented.