纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2014年
3期
221-228
,共8页
局部资料%变分同化%正则化%稳定性%收敛精度
跼部資料%變分同化%正則化%穩定性%收斂精度
국부자료%변분동화%정칙화%은정성%수렴정도
local observation data%variational data assimilation%regularization%stability%convergence rate
对于简化的一维扩散方程，在局部观测资料下，研究变分同化方法的稳定性。在变分同化中结合正则化方法，选择合适的正则化参数和稳定泛函，对预报模式进行修正，通过对预报精度进行先验估计，证明了该方法对于一维扩散方程的解的稳定性。修正补充相关计算结果，最后举出一个反例说明稳定性泛函的选取对于改进的变分同化方法实施的重要性。
對于簡化的一維擴散方程，在跼部觀測資料下，研究變分同化方法的穩定性。在變分同化中結閤正則化方法，選擇閤適的正則化參數和穩定汎函，對預報模式進行脩正，通過對預報精度進行先驗估計，證明瞭該方法對于一維擴散方程的解的穩定性。脩正補充相關計算結果，最後舉齣一箇反例說明穩定性汎函的選取對于改進的變分同化方法實施的重要性。
대우간화적일유확산방정，재국부관측자료하，연구변분동화방법적은정성。재변분동화중결합정칙화방법，선택합괄적정칙화삼수화은정범함，대예보모식진행수정，통과대예보정도진행선험고계，증명료해방법대우일유확산방정적해적은정성。수정보충상관계산결과，최후거출일개반례설명은정성범함적선취대우개진적변분동화방법실시적중요성。
The stability of variational data assimilation method with local observation data is researched for the simplified one-dimensional diffusion equation. The prediction value of the model is modified by using the combination of the regularization method with variational data assimilation method, and the prior estimate of the improved variational data assimilation methods are made in theories. By suitable choices of the regularization parameter and stable function, prove that the method is stability for the simplified one-dimensional diffusion equation. Some proofs and results are revised and complemented in this paper, and finally give an example to illustrate the importance of selecting for the stability functional on the improved variational data assimilation methods.
