一维扩散方程整体观测资料下的初值变分同化反演

本文考虑一维扩散方程的反问题,利用变分同化方法通过观测资料来确定方程中的未知初值,通过分析观测误差对于初值误差的影响,证明变分同化初值收敛于原问题的真实参数,并得到了参数的收敛精度。同时将得到的初值代入预报模式中,得到预报解,并分析了预报解的收敛性和预报误差。

The Variational Assimilation Method for the Inverse Problem of the Initial Condition in the One-dimensional Diffusion Equation

The variational assimilation method for the inverse problem of the initial conditionin the one-dimensional diffusion equation is studied in this paper. When the observationdata is given, the optimal initial condition of the model is got by using the variationaldata assimilation method. By analyzing of the impacts of the observational errors on theinitial condition, it has been approved that the assimilated initial condition convergences tothe true initial conditions and the convergence rate of the errors in assimilated initialconditions is got. And also the predicted solution convergences to the true solution, theconvergence rate of the errors in the predicted solution is obtained in this paper..