Penalty-scaling effects in nonsymmetric interior-penalty DG discretizations of viscous rotating shallow-water equations

2026/07/17 by Xue Zhang, Jingmin Xia, Xu Qian
#math.NA #cs.NA

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Abstract

We investigate how the scaling of the interior-penalty parameter affects nonsymmetric interior-penalty Galerkin (NIPG) discretizations of the viscous rotating shallow-water equations in geopotential variables. The hyperbolic terms are approximated by a local Lax--Friedrichs flux, while viscosity acts on the momentum variables through a penalty law μ_e=σh_e^-β. The standard choice β=1 and the super-penalized choice β=3 are compared with a symmetric interior-penalty Galerkin reference. For the diffusion form, we establish consistency, continuity for β≥ 1, and an exact coercivity identity in the momentum DG seminorm. Manufactured-solution tests show that super-penalization can recover the expected momentum L² accuracy, whereas the coupled geopotential variable need not exhibit the same improvement. Rotating and topography-aware tests further show that the standard scaling generally gives the better accuracy-cost compromise for the explicit implementation considered here.

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