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arXiv · 2602.22861

On $hp$-adaptive Structure-Preservion for the Cahn--Hilliard--Navier--Stokes Equations with Degenerate Mobility

Jimmy Kornelije Gunnarsson·Robert Klöfkorn
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Abstract

We develop structure-preserving discontinuous Galerkin methods for the Cahn-Hilliard-Navier-Stokes equations with degenerate mobility. The proposed SWIPD-L and SIPGD-L methods incorporate parametrized mobility fluxes with edge-wise mobility treatments for enhanced coercivity-stability control. We prove coercivity for the generalized trilinear form and demonstrate optimal convergence rates while preserving mass conservation, energy dissipation, and the discrete maximum principle. Comparisons with existing SIPG-L and SWIP-L methods confirm similar stability. Validation on $hp$-adaptive meshes for both standalone Cahn-Hilliard and coupled systems shows significant computational savings without accuracy loss.

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Jimmy Kornelije Gunnarsson, Robert Klöfkorn. 2026-02-26. On $hp$-adaptive Structure-Preservion for the Cahn--Hilliard--Navier--Stokes Equations with Degenerate Mobility. https://arxiv.org/abs/2602.22861

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