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This article presents families of spatial discretizations of the nonlinear rotating shallow‐water equations that conserve both energy and potential enstrophy. These are based on two‐dimensional mixed finite‐element methods and hence, unlike some finite‐difference methods, do not require an orthogonal grid. Numerical verification of the aforementioned properties is also provided.

Energy‐ and enstrophy‐conserving schemes for the shallow‐water equations, based on mimetic finite elements