Abstract
A non-overlapping domain decomposition method is developed for coupled Stokes-Darcy flows in irregular domains. The
Stokes region is discretized by standard Stokes finite elements while the Darcy region is discretized by the multipoint flux
mixed finite element method. The subdomain grids may not match on the interfaces and mortar finite elements are employed
to impose weakly interface continuity conditions. The interfaces can be curved and matching conditions are imposed via
appropriate mappings from physical grids to reference grids with flat interfaces. The global problem is reduced to a mortar
interface problem, which is solved by the conjugate gradient method. Each iteration involves solving subdomain problems of
either Stokes or Darcy type, which is done in parallel. Computational experiments are presented to illustrate the convergence
of the discretization and the condition number of the interface operator.
Keywords: non-overlapping domain decomposition; Stokes-Darcy flows; mixed finite element; multipoint flux
approximation; curved interface; mortar finite element

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