伪双曲型方程的混合控制体积方法  

A Mixed Covolume Method for Pseudo-Hyperbolic Equation

作　　者：方志朝[1] 李宏 罗振东[2] 

机构地区：[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

出　　处：《数学物理学报（A辑）》2013年第3期535-550,共16页Acta Mathematica Scientia

基　　金：国家自然科学基金(11061021,11061009);内蒙古高校科学研究项目(NJ10006)资助

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.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 con- structed by using the lowest order Raviart-Thomas mixed finite element space and introducing a transfer operator ~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.

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 

分 类 号：O242.21[理学—计算数学]