A posteriori error estimates for a Virtual Element Method for the Steklov eigenvalue problem. (1st November 2017)

• Record Type: Journal Article
• Authors: Mora, David; Rivera, Gonzalo; Rodríguez, Rodolfo
• Is Part Of: Computers & mathematics with applications. Volume 74:issue 9(2017)
• Page Start: 2172
• Page End: 2190
• Publication Date: 2017-11-01
• Subjects: Virtual element method -- A posteriori error estimates -- Steklov eigenvalue problem -- Polygonal meshes; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.05.016
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The paper deals with the a posteriori error analysis of a virtual element method for the Steklov eigenvalue problem. The virtual element method has the advantage of using general polygonal meshes, which allows implementing efficiently mesh refinement strategies. We introduce a residual type a posteriori error estimator and prove its reliability and global efficiency. Local efficiency estimates also hold, although in some elements they involve boundary terms that are not known to be locally negligible. We use the corresponding error estimator to drive an adaptive scheme. Finally, we report the results of a couple of numerical tests, that allow us to assess the performance of this approach.