A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian. (15th August 2017)

• Record Type: Journal Article
• Authors: Acosta, Gabriel; Bersetche, Francisco M.; Borthagaray, Juan Pablo
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 4(2017)
• Page Start: 784
• Page End: 816
• Publication Date: 2017-08-15
• Subjects: Finite elements -- Fractional Laplacian -- Nonlocal operators; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.05.026
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In Acosta etal. (2017), a complete n -dimensional finite element analysis of the homogeneous Dirichlet problem associated to a fractional Laplacian was presented. Here we provide a comprehensive and simple 2D MATLAB ® finite element code for such a problem. The code is accompanied with a basic discussion of the theory relevant in the context. The main program is written in about 80 lines and can be easily modified to deal with other kernels as well as with time dependent problems. The present work fills a gap by providing an input for a large number of mathematicians and scientists interested in numerical approximations of solutions of a large variety of problems involving nonlocal phenomena in two-dimensional space.