Energy conserving Galerkin finite element schemes for the primitive equations of numerical weather prediction
This paper presents some energy conserving finite element schemes for the primitive meteorological equations. Schemes are formulated for the two- dimensional shallow water equations. All schemes presented can easily be generalized to energy conserving schemes of the sigma-system equations. One of the schemes requires a relation between the approximation spaces for pressure and temperature. Another scheme uses only linear elements for all fields, and therefore may be a good candidate for implementation in large models. Since the schemes use only general relations between the basis function spaces, the developments are valid for other Galerkin schemes, such as the spectral method or the parameter fluid models. Questions of practical implementation are discussed only for the use of linear finite elements for the velocity field.
energy conserving finite element schemes
scientific article; zbMATH DE number 3982747