亚网格微尺度相互作用的分辨率增强了非自治偏微分方程的离散化
Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations
摘要：
中心流形理论对非线性非自治偏微分\difference方程的粗粒度、宏观尺度、空间离散化给出了新的支持。将物理域划分为重叠的宏观尺度元素，使该方法能够解决显着的亚网格微观尺度结构和相邻元素之间的相互作用。这种方法的关键方面是，中心流形理论组织的详细的亚网格微尺度结构的分辨率通过非线性动力学内和相邻元素之间的相互作用。这里开发的技术和理论可以应用到健全的离散在宏观尺度上许多耗散非自治偏微分\difference方程，如强迫Burgers方程，通过这里作为一个说明性的例子。
英文摘要：
Coarse grained, macroscale, spatial discretisations of nonlinear nonautonomous partial differential\difference equations are given novel support by centre manifold theory. Dividing the physical domain into overlapping macroscale elements empowers the approach to resolve significant subgrid microscale structures and interactions between neighbouring elements. The crucial aspect of this approach is that centre manifold theory organises the resolution of the detailed subgrid microscale structure interacting via the nonlinear dynamics within and between neighbouring elements. The techniques and theory developed here may be applied to soundly discretise on a macroscale many dissipative nonautonomous partial differential\difference equations, such as the forced Burgers' equation, adopted here as an illustrative example.
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