27 citations · 118 across the 26 of their papers we have counts for
4 papers · 1 filter
Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation
Hailiang Liu, Peimeng Yin
In this paper, we introduce novel discontinuous Galerkin (DG) schemes for the Cahn-Hilliard equation, which arises in many applications. The method is designed by integrating the m…
Unconditionally energy stable DG schemes for the Swift-Hohenberg equation
Hailiang Liu, Peimeng Yin
The Swift-Hohenberg equation as a central nonlinear model in modern physics has a gradient flow structure. Here we introduce fully discrete discontinuous Galerkin (DG) schemes for…
A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems
Hailiang Liu, Peimeng Yin
A novel discontinuous Galerkin (DG) method is developed to solve time-dependent bi-harmonic type equations involving fourth derivatives in one and multiple space dimensions. We pre…
General superpositions of Gaussian beams and propagation errors
Hailiang Liu, James Ralston, Peimeng Yin
Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful…