数值求解二维Sine-Gordon方程的C^0P_1时间递进方法

A C^0P_1 Time Stepping Method for Solving 2D Sine-Gordon Equations

提出了基于局部线性化的连续分片线性(以下简称C^0P_1)时间递进方法^([1])求解二维sine-Gordon方程的数值方法.首先在时间方向采用连续分片线性有限元离散,通过对sine-Gordon方程中各项分别采用显式或隐式线性化插值,导出时间半离散格式.再在空间方向利用有限元方法^([2])离散得到全离散格式.若干数值试验证明了该方法的有效性.

This paper proposes a continuous piecewise linear （called C0P_1 for short）time stepping method[1] combined with local linearization for solving 2D sine-Gordon equations. First of all, the sine-Gordon equations are discretized in time direction by a linear continuous Galerkin method combined with the explicit or implicit local linearization,leading to a semi-discrete scheme. Furthermore,a full-discrete scheme is obtained by spatial discretization with the finite element method[2]. Several numerical experiments are given to perform the effectiveness of the method.