  The present work focuses on the geometric parametrization and the reduced
order modeling of the Stokes equation. We discuss the concept of a parametrized
geometry and its application within a reduced order modeling technique. The
full order model is based on the discontinuous Galerkin method with an interior
penalty formulation. We introduce the broken Sobolev spaces as well as the weak
formulation required for an affine parameter dependency. The operators are
transformed from a fixed domain to a parameter dependent domain using the
affine parameter dependency. The proper orthogonal decomposition is used to
obtain the basis of functions of the reduced order model. By using the Galerkin
projection the linear system is projected onto the reduced space. During this
process, the offline-online decomposition is used to separate parameter
dependent operations from parameter independent operations. Finally this
technique is applied to an obstacle test problem.The numerical outcomes
presented include experimental error analysis, eigenvalue decay and measurement
of online simulation time. Keywords: Discontinuous Galerkin method, Stokes
flow, Geometric parametrization, Proper orthogonal decomposition
