耦合非线性抛物方程组的H1-Galerkin混合元方法
H1-Galerkin Mixed Element Method for the Coupling Nonlinear Parabolic Partial Equations
DOI: 10.12677/pm.2011.12016, PDF, HTML,    国家自然科学基金支持
作者: 王金凤：内蒙古财经学院统计与数学学院，呼和浩特；刘洋, 李宏：内蒙古大学数学科学学院，呼和浩特；李晓瑜：内蒙古工业大学理学院，呼和浩特
关键词: 耦合非线性抛物方程组；H1-Galerkin混合元方法；向后欧拉方法；最优阶误差估计
Coupling Nonlinear Parabolic Partial Equations;H1-Galerkin Mixed Element Method; Backward Euler’s Method; Optimal Error Estimates
摘要: 利用H1-Galerkin混合有限元方法讨论耦合非线性抛物方程组，得到一维情形的半离散和全离散格式和未知存量函数和它的梯度的最优收敛阶误差估计，而且不用验证LBB相容性条件。最后，通过数值例子验证了该算法的可行性。
Abstract: An H1-Galerkin mixed finite element method is discussed for the coupling nonlinear parabolic partial equations. Semidiscrete and fully discrete schemes and optimal error estimates of the scalar unknown and its gradient are derived for problems in one space dimension, and it dose not require the LBB consistency condition. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.
文章引用：王金凤, 刘洋, 李宏, 李晓瑜. 耦合非线性抛物方程组的H1-Galerkin混合元方法[J]. 理论数学, 2011, 1(2): 73-79. http://dx.doi.org/10.12677/pm.2011.12016

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