25 citations · 68 across the 6 of their papers we have counts for
7 papers
Energy stable Runge-Kutta discontinuous Galerkin schemes for fourth order gradient flows
Hailiang Liu, Peimeng Yin
We present unconditionally energy stable Runge-Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows. Our algorithm is geared toward arb…
A finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain
Hengguang Li, Peimeng Yin, Zhimin Zhang
In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-ord…
Regularity and finite element approximation for two-dimensional elliptic equations with line Dirac sources
Hengguang Li, Xiang Wan, Peimeng Yin +1
We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measur…
On the SAV-DG method for a class of fourth order gradient flows
Hailiang Liu, Peimeng Yin
For a class of fourth order gradient flow problems, integration of the scalar auxiliary variable (SAV) time discretization with the penalty-free discontinuous Galerkin (DG) spatial…
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…