四阶抛物型积分微分方程的H1-Galerkin混合元方法
H1-Galerkin Mixed Element Method for Fourth-Order Parabolic Integro-Differential Equation
DOI: 10.12677/AAM.2016.53043, PDF, HTML, XML, 下载: 2,359  浏览: 8,566  国家自然科学基金支持
作者: 李岩, 侯雅馨：内蒙古大学数学科学学院，内蒙古 呼和浩特
关键词: 四阶抛物型积分微分方程；H1-Galerkin混合有限元方法；误差估计；稳定性分析；Fourth-Order Parabolic Integral Differential Equations； H1-Galerkin Mixed Finite Element Method； Error Estimation； Stability Analysis
摘要: 本文讨论四阶抛物型积分微分方程的H1-Galerkin混合有限元方法，研究一维情形下带有四阶空间导数项的抛物型积分微分方程H1-Galerkin混合有限元数值方法。根据方程的特点，通过三个适当中间变量的引入，可将原四阶问题化为一个仅含有一阶导数的耦合方程组系统。对系统半离散和全离散格式的最优收敛误差估计给出详细的分析证明，并推导了全离散系统的稳定性结果。
Abstract: In this paper, an H1-Galerkinmixed element method is considered for one-dimensional fourth-or- der integro-differential equation of parabolic type. According to the characteristics of the consi-dered equation, the three auxiliary variables are introduced, then the original fourth-order prob-lem can be split into the coupled system with first order derivative. Some optimal error estimates for both semi-and fully discrete scheme are proved and the stability for fully discrete system is also derived.
文章引用：李岩, 侯雅馨. 四阶抛物型积分微分方程的H1-Galerkin混合元方法[J]. 应用数学进展, 2016, 5(3): 349-359. http://dx.doi.org/10.12677/AAM.2016.53043

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