论文标题
有限元方法在bakhvalov型网状网格上的超级细度，用于两个参数的奇异扰动问题
Supercloseness of finite element method on a Bakhvalov-type mesh for a singularly perturbed problem with two parameters
论文作者
论文摘要
在本文中，将Bakhvalov型网格上的线性有限元方法应用于具有两个参数的奇异扰动问题。问题的解决方案存在两个指数边界层。引入了一种新的插值，在构建和分析中很简单，用于收敛分析。此外，我们发现Bakhvalov型网状本身与较弱的指数层之间存在微妙的关系，并获得了有趣的结果。最后，我们证明了拉格朗日插值和数值解决方案之间的超熟度结果。数值测试证实了我们的理论结果。
In this paper, the linear finite element method on a Bakhvalov-type mesh is applied to a singularly perturbed problem with two parameters. The solution of the problem exists two exponential boundary layers. A new interpolation, which is simple in construction and analysis, is introduced for convergence analysis. Furthermore, we find a subtle relationship between the Bakhvalov-type mesh itself and the weaker exponential layer and obtain an interesting result. Finally, we prove a supercloseness result between the Lagrange interpolation and the numerical solution. Numerical tests confirm our theoretical results.
