论文标题
线性化连续Galerkin HP-FEM应用于非线性初始值问题
Linearized Continuous Galerkin hp-FEM Applied to Nonlinear Initial Value Problems
论文作者
论文摘要
在本说明中，我们将任意顺序的连续盖尔金时步进方法视为非线性初始值问题的离散方案。此外，我们通过将一般线性化过程应用于非线性离散方案（包括简化的牛顿解决方案程序），为离散解决方案开发并概括了现有的现有结果。特别是，通过在本地选择足够的小时步骤来暗示提出的存在结果。此外，已建立的存在结果与局部近似顺序无关。此外，我们将看到所提出的解决方案方案能够显着减少迭代次数。最后，基于现有且众所周知的离散解决方案的先验误差估计，我们提出了一些数值实验，这些实验强调了本注释的提议结果。
In this note we consider the continuous Galerkin time stepping method of arbitrary order as a possible discretization scheme of nonlinear initial value problems. In addition, we develop and generalize a well known existing result for the discrete solution by applying a general linearizing procedure to the nonlinear discrete scheme including also the simplified Newton solution procedure. In particular, the presented existence results are implied by choosing sufficient small time steps locally. Furthermore, the established existence results are independent of the local approximation order. Moreover, we will see that the proposed solution scheme is able to significantly reduce the number of iterations. Finally, based on existing and well known a priori error estimates for the discrete solution, we present some numerical experiments that highlight the proposed results of this note.
