Energy- and enstrophy-conserving schemes for the shallow-water equations, based on mimetic finite elements - McRae,ATT; Cotter,CJ (Quarterly Journal of the Royal Meteorological Society, 2014)
This paper presents a family of spatial discretisations of the nonlinearrotating shallow-water equations that conserve both energy and potentialenstrophy. These are based on two-dimensional mixed finite element methods, andhence, unlike some finite difference methods, do not require an orthogonalgrid. Numerical verification of the aforementioned properties is also provided.