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Mixed Covolume Methods for a Damped Sine-Gordon Equation on Triangular Grids

方志朝, 李宏
FANG Zhichao*, LI Hong**

内蒙古大学数学科学学院, 呼和浩特, 内蒙古, 010021
School of Mathematical Sciences, Inner Mongolia University, Hohhot, Inner Mongolia, 010021, P. R. China

收稿日期: 2011-09-29
出版日期: 2013-08-25
DOI: 10.11845/sxjz.20130402b


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摘要 本文利用混合控制体积方法在三角网格剖分下求解阻尼Sine-Gordon方程. 通过使用最低阶 Raviart-Thomas 混合有限元空间和引入迁移算子把解函数空间映射成试探函数空间, 构造了半离散和全离散的混合控制体积格式. 根据阻尼 Sine-Gordon 方程的特点引入广义混合控制体积投影, 利用迁移算子的性质和广义混合控制体积投影得到了最优阶误差估计.最后, 给出数值算例验证理论分析结果.
关键词 阻尼Sine-Gordon方程混合控制体积方法全离散格式最优阶误差估计    
Abstract:The mixed covolume method is analyzed for a damped Sine-Gordon equation on triangular grids. Semi-discrete and fully-discrete mixed covolume schemes are constructed by using the lowest order Raviart-Thomas mixed finite element space and introducing a transfer operator $\gamma_h$ which maps the trial function space into the test function space. According to the characteristics of the damped Sine-Gordon equation, the generalized mixed covolume projection is introduced, then optimal error estimates are derived by using the properties of the transfer operator and generalized mixed covolume projection. Finally, a numerical example is given to confirm the theoretical results.
Key wordsmixed covolume method    fully-discrete scheme    optimal error estimate
基金资助:Supported by NSFC (No. 11061021), the Science Research of Inner Mongolia Advanced Education (No. NJ10016, No. NJZZ12011), and the National Science Foundation of Inner Mongolia Province (No. 2011BS0102, No. 2012MS0106)
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