抛物型积分微分方程对称修正的有限体积元方法(英文)  

Symmetric Modified Finite Volume Element Methods for Parabolic Integro-Differential Equations

作　　者：杨青[1] 

机构地区：[1]山东师范大学数学科学学院,山东250014

出　　处：《工程数学学报》2008年第3期520-530,共11页Chinese Journal of Engineering Mathematics

基　　金：The Natural Science Foundation of Shandong Province(Z2006A02).

摘　　要：一般有限体积元方法所产生的系数矩阵是不对称的,通过将双线性形式对称化,并对由此产生的误差项进行修正,可得到对称修正的有限体积元法。对抛物型积分微分方程使用对称修正的有限体积元法进行数值模拟,通过理论分析,得到了最优的H1模和L2模误差估计结果。还证明了对称修正的有限体积元法的解与有限体积元解之间相差一个高阶项。数值例子验证了方法的可行性和有效性。The finite volume element method generally results in non-symmetric linear system. By symmetrizing the bilinear forms and then correcting the scheme, we obtain a kind of symmetric modified finite volume element methods. This method is applied to discrete twodimensional parabolic integro-differential equations. Optimal error estimates in H^1- and L^2-norm are derived for semi-discrete scheme. It is also proved that the difference between the solutions of the finite volume element method and the symmetric finite volume element method is a high order term. The numerical example shows that the method is feasible and effective.

关 键 词：抛物型积分微分方程 初边值问题 对称修正有限体积元 误差估计 

分 类 号：O241[理学—计算数学]