Numerical simulation for 2D sedimentation model by an upwind discontinuous Galerkin procedure (Q1992509)

Summary: We reformulate the mathematical model for the 2D sedimentation in an estuary as a coupled nonlinear differential system. Combining the mass-conservation character of the discontinuous Galerkin method and the jump-capturing property of \textit{Lesaint}- \textit{Raviart} upwind technique, we design an upwind discontinuous Galerkin finite element method, which obeys the local mass conservation and possesses good stability. Our theoretical analysis shows that there exists a unique solution to the numerical procedure and the discrete solution permits \(\mathcal{O}(h^k + \Delta t)\) convergence rate. Numerical experiments are conducted to verify our theoretical findings. This may provide a theoretical principle for better understanding of the mechanism and morphological characters of sedimentation at estuaries.