  We derive and analyse well-posed boundary conditions for the linear shallow
water wave equation. The analysis is based on the energy method and it
identifies the number, location and form of the boundary conditions so that the
initial boundary value problem is well-posed. A finite volume method is
developed based on the summation-by-parts framework with the boundary
conditions implemented weakly using penalties. Stability is proven by deriving
a discrete energy estimate analogous to the continuous estimate. The continuous
and discrete analysis covers all flow regimes. Numerical experiments are
presented verifying the analysis.
