【摘要】：本文針對(duì)二階橢圓微分方程反源問(wèn)題,討論了由文[22]引入的極小問(wèn)題的高次有限元方法,建立了基于全局測(cè)量數(shù)據(jù)的反源問(wèn)題的兩種二次有限元變分問(wèn)題解函數(shù)的誤差估計(jì)理論.數(shù)值實(shí)驗(yàn)表明,當(dāng)擾動(dòng)量可忽略時(shí),兩種二次有限元變分問(wèn)題解函數(shù)的誤差階均高于線性元情形;當(dāng)擾動(dòng)量不可忽略時(shí),在某種參數(shù)的適當(dāng)選取下,二次有限元解函數(shù)的誤差關(guān)于擾動(dòng)量的下降率高于線性元情形.實(shí)驗(yàn)結(jié)果驗(yàn)證了誤差估計(jì)的正確性.進(jìn)一步,給出基于局部測(cè)量數(shù)據(jù)的反源問(wèn)題的高次元算法.數(shù)值結(jié)果表明,當(dāng)局部測(cè)量數(shù)據(jù)的延拓函數(shù)在子區(qū)域邊界上滿足一定的光滑性時(shí),該算法是穩(wěn)健的.
[Abstract]:In this paper, for the inverse source problem of second order elliptic differential equation, we discuss the high order finite element method for the minimal problem introduced in [22]. The error estimation theory of solutions to two quadratic finite element variational problems based on global measurement data is established. Numerical experiments show that when the disturbance is negligible, the error order of the solutions of the two quadratic finite element variational problems is higher than that of the linear element. When the disturbance can not be ignored, the error of quadratic finite element solution is higher than that of linear element when the parameter is properly selected. The experimental results verify the correctness of the error estimation. Furthermore, a high order algorithm for inverse source problem based on local measurement data is presented. The numerical results show that the algorithm is robust when the continuation function of the local measured data satisfies certain smoothness on the subregion boundary.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O241.82

【參考文獻(xiàn)】

相關(guān)期刊論文 前3條

1 宋世俊;黃建國(guó);;一個(gè)反源問(wèn)題的極小化能量泛函正則化方法[J];上海交通大學(xué)學(xué)報(bào);2011年12期

2 張曦;朱昌雄;馮廣達(dá);朱紅惠;郭萍;;基于擬桿菌特異性16S rRNA基因的塘壩型飲用水污染溯源研究[J];農(nóng)業(yè)環(huán)境科學(xué)學(xué)報(bào);2011年09期

3 鄭曉勢(shì),張玉海;二維橢圓型偏微分方程的反源問(wèn)題[J];山東大學(xué)學(xué)報(bào)(自然科學(xué)版);2001年04期

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本文編號(hào)：2407060