A C0-hybrid interior penalty method for the nematic Helmholtz-Korteweg equation

The nematic Helmholtz-Korteweg equation is a fourth-order scalar PDE modelling time-harmonic acoustic waves in nematic Korteweg fluids, such as nematic liquid crystals. Conforming discretizations typically require C1-conforming elements, for example the Argyris element, whose implementation is notoriously challenging - especially in three dimensions - and often demands a high polynomial degree. 
In this talk, we consider an alternative non-conforming C0-hybrid interior penalty method that is both stable and convergent for any polynomial degree greater than two. Classical C0-interior penalty methods employ an H1-conforming subspace and treat the non-conformity with respect to H2 with discontinuous Galerkin techniques. Building on this idea, we use hybridization techniques to improve the computational efficiency of the discretization. We provide a brief overview of the numerical analysis and show numerical examples, demonstrating the method's ability to capture anisotropic propagation of sound in two and three dimensions.