Name
Abstract | ||
|---|---|---|
In this paper, we propose several novel recovery based finite element methods for the 2D Cahn-Hilliard equation. One distinguishing feature of those methods is that we discretize the fourth-order differential operator in a standard C0 linear finite elements space. Precisely, we first transform the fourth-order Cahn-Hilliard equation to its variational formulation in which only first-order and second-order derivatives are involved and then we compute the first and second-order derivatives of a linear finite element function by a least-squares fitting recovery procedure. When the underlying mesh is uniform meshes of regular pattern, our recovery scheme for the Laplacian operator coincides with the well-known five-point stencil. Another feature of the methods is some special treatments on Neumann type boundary conditions for reducing computational cost. The optimal-order convergence and energy stability are numerically proved through a series of benchmark tests. The proposed method can be regarded as a combination of the finite difference scheme and the finite element scheme. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.jcp.2019.01.056 | Journal of Computational Physics |
Keywords | Field | DocType |
Hessian recovery,Cahn-Hilliard equation,Phase separation,Recovery based,Superconvergence,Linear finite element | Discretization,Boundary value problem,Mathematical analysis,Cahn–Hilliard equation,Stencil,Hessian matrix,Differential operator,Finite element method,Mathematics,Laplace operator | Journal |
Volume | ISSN | Citations |
386 | 0021-9991 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Minqiang Xu | 1 | 76 | 11.77 |
| hailong guo | 2 | 19 | 3.49 |
| Qingsong Zou | 3 | 96 | 13.99 |