伪双曲型方程的混合控制体积方法

数学物理学报 ›› 2013, Vol. 33 ›› Issue (3): 535-550.

伪双曲型方程的混合控制体积方法

方志朝¹|李宏¹|罗振东²

1.内蒙古大学数学科学学院呼和浩特 010021;
2.华北电力大学数理学院北京 102206

收稿日期:2011-11-19 修回日期:2013-02-05 出版日期:2013-06-25 发布日期:2013-06-25
基金资助:
国家自然科学基金(11061021, 11061009)和内蒙古高校科学研究项目(NJ10006)资助

A Mixed Covolume Method for Pseudo-Hyperbolic Equation

FANG Zhi-Chao¹, LI Hong¹, LUO Zhen-Dong²

1.School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021;
2.School of Mathematics and Physics, North China Electric Power University, Beijing 102206

Received:2011-11-19 Revised:2013-02-05 Online:2013-06-25 Published:2013-06-25
Supported by:
国家自然科学基金(11061021, 11061009)和内蒙古高校科学研究项目(NJ10006)资助

摘要/Abstract

摘要：

利用混合控制体积方法在三角形网格剖分下求解一类伪双曲型方程. 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. 根据伪双曲型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了理论结果以及该方法的有效性.

关键词: 伪双曲型方程, 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 class of second-order pseudo-hyperbolic equations 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 γ_h that maps the trial function space into the test function space. According to the characteristics of the pseudo-hyperbolic equation, 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, numerical experiments are given to verify the theoretical results and the effectiveness of the proposed method.

Key words: Pseudo-hyperbolic equation, Mixed covolume method, Fully-discrete scheme, Optimal error estimate

中图分类号:

65M08

方志朝, 李宏, 罗振东. 伪双曲型方程的混合控制体积方法[J]. 数学物理学报, 2013, 33(3): 535-550.

FANG Zhi-Chao, LI Hong, LUO Zhen-Dong. A Mixed Covolume Method for Pseudo-Hyperbolic Equation[J]. Acta mathematica scientia,Series A, 2013, 33(3): 535-550.

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