论文标题
不连续的彼得 - 盖尔金有限元方法的最佳近似空间
Optimal approximation spaces for discontinuous Petrov-Galerkin finite element methods
论文作者
论文摘要
某些Petrov-Galerkilkin方案是给定网格上变异问题的固有稳定表述。这种稳定性主要是通过计算给定近似空间的最佳测试基础获得的。此外，这些Petrov-Galerkilkin方案配备了可靠的后验误差估计，这使它们成为网状适应性的理想候选者。人们可以将这些Petrov-Galerkin方案不仅扩展到具有最佳测试空间，而且还具有相对于溶液的当前估计值的最佳近似空间。这些扩展是本文的主要重点。在本文中，我们提供了一种驱动网格适应性的方法，以产生最佳的网格，以解决解决方案功能和输出功能，我们通过数值实验证明了这些功能。
Certain Petrov-Galerkin schemes are inherently stable formulations of variational problems on a given mesh. This stability is primarily obtained by computing an optimal test basis for a given approximation space. Furthermore, these Petrov-Galerkin schemes are equipped with a robust a posteriori error estimate which makes them an ideal candidate for mesh adaptation. One could extend these Petrov-Galerkin schemes not only to have optimal test spaces but also optimal approximation spaces with respect to current estimates of the solution. These extensions are the main focus of this article. In this article, we provide a methodology to drive mesh adaptation to produce optimal meshes for resolving solution features and output functionals which we demonstrate through numerical experiments.
