论文标题
严格的FEM 1D汉堡方程
Rigorous FEM for 1D Burgers equation
论文作者
论文摘要
我们提出了一种通过使用有限元方法（FEM）的时间严格地集成耗散PDE的方法。该技术基于对FEM空间的Galerkin投影，并估计了残留项。在定期强迫一维汉堡方程的情况下说明了所提出的方法。对于强迫的两个特定选择，我们证明了周期性的全球吸引轨迹的存在，并在其形状上提供了精确的界限。
We propose a method to integrate dissipative PDEs rigorously forward in time with the use of Finite Element Method (FEM). The technique is based on the Galerkin projection on the FEM space and estimates on the residual terms. The proposed approach is illustrated on a periodically forced one-dimensional Burgers equation with Dirichlet conditions. For two particular choices of the forcing we prove the existence of the periodic globally attracting trajectory and give precise bounds on its shape.
