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中文摘要：
该文研究了三维抛物方程有限差分格式的解空间，利用奇异值分解求出解空间的一组POD（proper orthogonal decomposition）基，结合Galerkin投影方法导出了三维抛物方程有限差分格式具有较高精度的低维模型，并给出了POD格式解和有限差分格式解的误差估计．数值例子表明POD格式解和有限差分格式解的误差与理论结果是一致的，从而验证了POD方法的有效性．
英文摘要：
In this article, the solution space of three-dimensional parabolic equation finite difference scheme is studied. Firstly a group of proper orthogonal decomposition （POD） bases of solution space is obtained by using singular value decomposition. Secondly, by combining the Galerkin projection method, the finite difference scheme of three-dimensional parabolic equation is converted into a low dimensional mode with higher precise. Then, the error between the finite difference scheme solution and the POD scheme solution is presented. And it is shown by the numerical results that the error between the finite difference scheme solution and the POD scheme solution is consistents with theoretical results. Therefore, the POD method is effective and feasible
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