Jimmy Kornelije Gunnarsson presenting Discontinuous Galerkin Weighted Interior Penalty Methods for the Cahn—Hilliard Equations

Abstract:

Symmetric Weighted Interior Penalty (SWIP) discretization, was
introduced by (Ern et al., 2008) and applied to the Cahn—Hilliard
equations in (Gunnarsson & Klöfkorn, 2026), where a specific weight
option was proposed and compared to other schemes which numerically
provide evidence of structure preservation. For the newly developed
scheme a discrete maximum principle, mass conservation can be shown and
energy dissipation is observed. In this talk we present recent findings
both on the theoretical level and on the numerical level. We further
provide some generalizations which follow from coupling via advection.