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



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.