论文标题
一类转折点问题的均匀收敛性彼得 - 盖尔金方法
A Uniform Convergent Petrov-Galerkin method for a Class of Turning Point Problems
论文作者
论文摘要
在本文中，我们提出了一种基于Petrov-Galerkin有限元方法（PGFEM）的一个维点问题的数值方法。我们首先通过单个边界转折点对转折点问题进行先验估计。然后，我们使用PGFEM来解决它，其中测试功能是分段近似双重问题的解决方案。我们证明，当我们选择双重问题作为测试函数的确切解决方案时，我们的方法在$ l^\ infty $ norm和能量规范中具有一阶收敛率。数值结果表明，我们的方案对于具有不同类型的奇异性的转折点问题有效，并且收敛性与我们的理论结果一致。
In this paper, we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method (PGFEM). We first give a priori estimate for the turning point problem with a single boundary turning point. Then we use PGFEM to solve it, where test functions are the solutions to piecewise approximate dual problems. We prove that our method has a first-order convergence rate in both $L^\infty$ norm and an energy norm when we select the exact solutions to dual problems as test functions. Numerical results show that our scheme is efficient for turning point problems with different types of singularities, and the convergency coincides with our theoretical results.
