We present a supplementary variable method (SVM) for developing structure-preserving numerical approximations to a partial differential equation system with deduced equations. The PDE system with deduced equations constitutes an over-determined, yet consistent and structurally unstable system of equations. We augment a proper set of supplementary variables to the over-determined system to make it well-determined with a stable structure. We then discretize the modified system to arrive at a structure-preserving numerical approximation to the over-determined PDE system. We illustrate the idea using a dissipative network generating partial differential equation model by developing an energy-dissipation-rate preserving scheme. We then simulate the network generating phenomenon using the numerical scheme. This numerical method is so general that it applies literally to any PDE systems with deduced equations.

我们提出了一种补充变量方法（SVM），用于开发具有推导方程的偏微分方程系统的保结构数值逼近。具有推导方程的PDE系统构成了一个超定的，但一致且结构不稳定的方程系统。我们为超定系统增加了一组适当的补充变量，以使其结构稳定。然后，我们离散化修改后的系统，以得出与结构超确定的PDE系统近似的保留结构的数值近似值。我们通过开发耗能率保持方案，使用耗散网络生成偏微分方程模型来说明这一想法。然后，我们使用数值方案模拟网络生成现象。