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A tale of two elements: PNC1 - P1 and RT0
Hanert, E.; Le Roux, D.Y.; Pietrzak, J.D. (2009). A tale of two elements: PNC1 - P1 and RT0. Ocean Modelling 28(1-3): 24-33. http://dx.doi.org/10.1016/j.ocemod.2008.07.002
In: Ocean Modelling. Elsevier: Oxford. ISSN 1463-5003; e-ISSN 1463-5011, more
Peer reviewed article  
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Author keywords
    Shallow water equations; Finite element method; Propagation factor; Consistency
Authors  Top 
  • Hanert, E., more
  • Le Roux, D.Y., more
  • Pietrzak, J.D.
Abstract
    The PNC1 - 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 PNC1 - P1 element is better suited to purely hydrodynamical applications while the RT0 element might perform better for hydrological applications that require scalar transport calculations.
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