Discontinuous, continuous, and coupled finite element methods for shallow water flows

In this paper, we describe finite element methods for the numerical solution of the shallow water equations, based on coupling discontinuous and continuous approximations. While such coupling can be performed in several ways, we discuss one particular type of coupling, whereby the spatial domain is decomposed into two different regions, one where continuous approximating functions are used for all variables, and another where discontinuous functions are used. The algorithm is described and numerical results are presented for a one space dimensional example.