A free–energy stable p–adaptive nodal discontinuous Galerkin for the Cahn–Hilliard equation

A novel free–energy stable discontinuous Galerkin method is developed for the Cahn–Hilliard equation with non–conforming elements. This work focuses on dynamic polynomial adaptation (p–refinement) and constitutes an extension of by Manzanero et al. (2020) [8], which makes use summation–by–parts simultaneous–approximation term technique along Gauss–Lobatto points Bassi–Rebay 1 (BR1) scheme. The BR1 numerical flux accommodates elements, are connected through mortar method. scheme has been analytically proven to retain its stability when transitioning non-conforming Furthermore, a methodology perform introduced based knowledge location interface between phases. tested accuracy effectiveness series steady unsteady test cases. We freestream preservation primary quantity conservation curvilinear meshes. solve one–dimensional case initially examine adaptation. we study formation static bubble in two dimensions verify that solver maintained while degrees freedom decrease less than half compared uniform solution. Lastly, such as spinodal decomposition show same results recovered, 35% reduction two–dimensional considered 48% three–dimensional case.