Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
A two-level time-stepping method for layered ocean circulation models
Journal of Computational Physics
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
Journal of Computational Physics
Dispersion Analysis of Discontinuous Galerkin Schemes Applied to Poincaré, Kelvin and Rossby Waves
Journal of Scientific Computing
Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
Journal of Computational Physics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Journal of Computational Physics
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This paper is part of an effort to examine the application of discontinuous Galerkin (DG) methods to the numerical modeling of the general circulation of the ocean. One step performed here is to develop an integral weak formulation of the lateral pressure forcing that is suitable for usage with a DG method and with a generalized vertical coordinate that includes level, terrain-fitted, isopycnic, and hybrid coordinates as examples. This formulation is then tested, in special cases, with analyses of dispersion relations and numerical stability and with some computational experiments. These results suggest that the advantages of DG methods may significantly outweigh their disadvantages, in the settings tested here. This paper also outlines some other issues that need to be addressed in future work.