Finite element approximation of fractional Neumann problems. (7th September 2021)

• Record Type: Journal Article
• Authors: Bersetche, Francisco M; Borthagaray, Juan Pablo
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 4(2022)
• Page Start: 3207
• Page End: 3240
• Publication Date: 2021-09-07
• Subjects: FEM -- fractional Laplacian -- Neumann boundary condition; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drab064
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: 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.