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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, PP. 73-79

Keywords: 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

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Abstract:

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。
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.

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