Shock Capturing Data Assimilation Algorithm for 1D Shallow Water Equations

In this paper we propose a new data assimilation algorithm for shallow water equations in one dimension. The algorithm is based upon Discontinuous Galerkin spatial discretisation of shallow water equations (DG-SW model) and the continuous formulation of the minimax lter. The latter allows one to construct a robust estimate of the state of DG-SW model and computes worst-case bounds for the estimation error, provided the uncertain parameters belong to a given bounding set. Numerical studies show that, given sparse observations from numerical or physical experiments, the proposed algorithm quickly reconstructs the true solution even in the presence of shocks and unknown values of model parameters.