A tale of two elements: P1NC-P1 and RT0

The P1NC-P1 and RT0 finite element schemes are among the most promising low order elements for use in unstructured mesh marine and lake models. They are both free of spurious elevation modes, have good dispersive properties and have a relatively low computational cost. In this paper, we derive both finite element schemes in the same unified framework and discuss their respective qualities in terms of conservation, consistency, propagation factor and convergence rate. We also highlight the impact that the local variables placement can have on the model solution. The main conclusion that we can draw is that the choice between elements is highly application dependent. We suggest that the P1NC-P1 element is better suited to purely hydrodynamical applications while the RT0 element might perform better for hydrological applications that require scalar transport calculations.