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二阶线性双曲方程的H1-Galerkin扩展混合有限元方法

An H^1 - GALERKIN EXPANDED MIXED FINITE ELEMENT METHOD FOR LINEAR HYPERBOLIC EQUATION
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摘要 采用H1-Galerkin扩展混合有限元法数值模拟二阶线性双曲方程，该方法的优点在于有限元空间无需满足LBB限制条件，还可以同时高精度逼近压力、压力梯度和Darcy速度．另外，由于该方法不需要对渗透率系数求逆，可适用于求解低渗透率问题．论证表明，该方法具有对压力、压力梯度和Darcy速度的L^2-最优逼近估计． A linear hyperbolic equation of second order is simulated by an H^1 Galerkin expanded mixed finite element method. This new formulation can directly approximate three variables, that is, its gradient and its flux vector, and does not require the mixed finite element spaces satisfying the scalar unknown, the LBB consistence condition, as well as it is suitable for the problem within low permeability zone without inverting the permeability coeffcient. The optimal L^2 -estimates for these three variables are proved.
作者 王玮玮 陈焕贞
机构地区 山东师范大学数学科学学院
出处 《山东师范大学学报（自然科学版）》 CAS 2010年第1期1-6,共6页 Journal of Shandong Normal University(Natural Science)
基金 国家百然科学基金资助项目（10926100,10971254） 山东省自然科学基金资助项目（Y2007A14,ZR2009AZ003） 山东省优秀中青年科学家科研奖励基金资助项目（2008BS01008）.
关键词 二阶双曲方程 扩展混合有限元 H^1—Galerkin方法 最优误差估计 hyperbolic equation of second order expanded mixed method H^1 - Galerkin method optimal error estimate
分类号 O241.82 [理学—计算数学]
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参考文献12

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二级参考文献16

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共引文献16

山东师范大学学报（自然科学版）
2010年 第1期

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