论文标题
分数诺伊曼问题的有限元近似
Finite element approximation of fractional Neumann problems
论文作者
论文摘要
在本文中，我们考虑了连续的，分段线性有限元元素的neumann问题的近似值。我们分析了此类问题的薄弱表述，包括它们的适当性和解决方案的渐近行为。我们解决了有限元离散化的融合并讨论该方法的实现。最后，我们在一维域中介绍了几个数值实验，这些实验说明了该方法的性能以及解决方案的某些特性。
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and asymptotic behavior of solutions. We address the convergence of the finite element discretizations and discuss the implementation of the method. Finally, we present several numerical experiments in one- and two-dimensional domains that illustrate the method's performance as well as certain properties of solutions.
