ABSTRACT
Abstract Instead of developing an adaptive grid technique for some discretization method, we develop a discretization technique designed for grid adaptation. This so-called compatible scheme allows to translate the leading term of the local residual directly in terms of a local error in the numerical solution (the numerical modeling error). An error-dependent smoothing technique is used to ensure that higher-order error terms are negligible. The numerical modeling error is minimized by means of grid adaptation. Fully converged adapted grids with strong local refinements are obtained for a steady-state shallow-water application with a hydraulic jump. An unsteady application confirms the importance of taking the error in time into account when adapting the grid in space. We discuss the shortcomings of the present implementation and the remedies currently under development.
