Coercivity-constant treatment in earlier limiter-based schemes

Develop a rigorous, data-independent treatment of the coercivity constant for the FEM-L, SIPG-L, SWIP-L, and related SWIPD-L schemes (for p > 0), ensuring robust semi-positivity or coercivity without ad hoc or ambiguous parameter choices.

Background

The present work provides a mobility-independent coercivity result for its diffusion operator, contrasting with earlier formulations where the coercivity constant’s treatment is unclear.

Clarifying and proving appropriate coercivity bounds for those earlier limiter-based schemes would strengthen their theoretical foundations and support fair comparisons.

References

It is also unclear how to properly treat the coercivity constant, as can be seen by comparing Theorem \ref{thm:coercivity} to Theorem 3.2.

— A Discontinuous Galerkin Scheme for the Cahn-Hilliard Equations with Discrete Maximum Principle for Arbitrary Polynomial Order  (2604.00988 - Gunnarsson et al., 1 Apr 2026) in Subsection "Comparison to other schemes", Section 4 (item 3)