论文标题
链接离散和连续扩散模型：适合和稳定的有限元离散
Linking discrete and continuum diffusion models: Well-posedness and stable finite element discretizations
论文作者
论文摘要
在数学建模的背景下，整合不同性质的模型有时很方便。但是，即使个人模型得到充分理解，这些类型的组合也可能会遇到困难，尤其是与合奏的合适性有关。在本文中，我们着重于结合两类不同的扩散模型：第一个模型在连续体中定义的一个基于离散方程式，该模型将解决方案的平均值连接到偏置子域而定。对于固定问题，我们显示了链接问题的无条件稳定性，然后在使用混合有限元元素来近似连续体上的模型时，其离散的对应物的稳定性和收敛性。理论结果通过数值示例突出显示，以说明链接扩散模型的效果。作为综上的结果，我们表明，本文中介绍的方法可用于通过不完整的数据来推断扩散问题的解决方案。
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in relation to the well-posedness of the ensemble. In this article, we focus on combining two classes of dissimilar diffusive models: the first one defined over a continuum and the second one based on discrete equations that connect average values of the solution over disjoint subdomains. For stationary problems, we show unconditional stability of the linked problems and then the stability and convergence of its discretized counterpart when mixed finite elements are used to approximate the model on the continuum. The theoretical results are highlighted with numerical examples illustrating the effects of linking diffusive models. As a side result, we show that the methods introduced in this article can be used to infer the solution of diffusive problems with incomplete data.
