Multiscale finite element method in a shallow water model

The multiscale finite element method (MsFEM) was originally proposed for stationary (elliptic) or quasi-stationary (parabolic) problems. It was extended to linear transport-dominated problems, utilizing a semi-Lagrangian subgrid reconstruction (SLMsR) approach. In this presentation we introduce the extension of the method to coupling non-linear systems of hyperbolic equations. To demonstrate the accuracy and applicability of SLMrS we use a shallow water model, where we discretize the momentum equation on a fine mesh and inform the coarse-mesh continuity equation of subgrid-scale features by using a multiscale basis. We show accuracy and convergence of the new method for smooth and non-smooth test cases.