Allen-Cahn方程弱形式的勒让德配置法及基于张量积的矩阵形式

The Legendre Collocation Method in the Weak Form and Matrix Formulation Based on Tensor Product for Allen-Cahn Equation

给出了Allen-Cahn方程弱形式的勒让德配置法的全离散格式,并对稳定性进行了分析.在适当的稳定性条件下,证明了给出的格式是能量稳定的.然后利用勒让德微分矩阵和Gauss-Lobatto积分的性质,全离散的勒让德配置格式被转化为矩阵方程,再利用张量积转化为线性代数方程组.

In this paper, the full discrete Legendre collocation methods in the weak form for Allen-Cahn equation are proposed and the stability analysis is carried out. It is shown that the schemes are energy stable with reasonable stability conditions. In addition, the full discrete Legendre collocation schemes are transformed into matrix form by using the properties of Legendre differentiation matrices and Gauss-Lobatto quadrature. And the matrix formulation based on tensor product is also obtained.