论文标题
高阶和较高规律性的各种时间离散
Variational Time Discretizations of Higher Order and Higher Regularity
论文作者
论文摘要
我们考虑了一个分散时间离散的家族，这些家族是不连续的Galerkin（DG）和连续Galerkin-Petrov（CGP）方法的概括。家庭的特征是两个参数。一个描述了多项式ANSATZ顺序，而另一个则与在子间隔两端的高阶搭配条件确保的全局平滑度相关联。呈现的方法提供了与DG或CGP相同的稳定性。前提是使用用于评估变异条件下积分的HERMITE类型的合适的正交规则，则将变异时间离散方法连接到特殊搭配方法。在这种情况下，我们将介绍错误估计，数值实验以及计算廉价的后处理，从而可以将准确性和全局平滑度提高一个顺序。
We consider a family of variational time discretizations that are generalizations of discontinuous Galerkin (dG) and continuous Galerkin-Petrov (cGP) methods. The family is characterized by two parameters. One describes the polynomial ansatz order while the other one is associated with the global smoothness that is ensured by higher order collocation conditions at both ends of the subintervals. The presented methods provide the same stability properties as dG or cGP. Provided that suitable quadrature rules of Hermite type for evaluating the integrals in the variational conditions are used, the variational time discretization methods are connected to special collocation methods. For this case, we will present error estimates, numerical experiments, and a computationally cheap postprocessing that allows to increase both the accuracy and the global smoothness by one order.
