一类抛物微分方程参数识别问题的二次有限体积元方法
The Quadratic Finite Volume Element Method for a Parameter Identification Problem of Parabolic Differential Equation
摘要:
针对一个具有附加条件的一类抛物微分方程的参数识别问题，首先提出了在空间上采用二次有限体积元法进行半离散，在时间方向上进行二次连续有限元全离散，导出了未知函数和控制参数稳定的数值解法，并给出了相应格式的误差分析，最后给出一个数值例子验证了所研究计算格式的稳定性和有效性。
Abstract:
In order to solve the problem of parameter identification for a class of parabolic differential equa-tions with additional conditions, the quadratic finite volume element method is proposed for semi-discretization in space and the quadratic continuous finite element method for complete discretization in time. The numerical solution of unknown function and control parameter stability is derived, and the error analysis of the corresponding format is given. Finally, a numerical example is given to verify the stability and effectiveness of the proposed scheme.
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