A finite element framework for some mimetic finite difference discretizations. (December 2015)

• Record Type: Journal Article
• Authors: Rodrigo, C.; Gaspar, F.J.; Hu, X.; Zikatanov, L.
• Is Part Of: Computers & mathematics with applications. Volume 70:issue 11(2015)
• Page Start: 2661
• Page End: 2673
• Publication Date: 2015-12
• Subjects: Mimetic finite differences -- Finite element methods -- Nédélec–Raviart–Thomas finite elements -- Multigrid -- Local Fourier analysis; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.07.012
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this work we derive equivalence relations between mimetic finite difference schemes on simplicial grids and modified Nédélec–Raviart–Thomas finite element methods for model problems in H ( curl ) and H ( div ) . This provides a simple and transparent way to analyze such mimetic finite difference discretizations using the well-known results from finite element theory. The finite element framework that we develop is also crucial for the design of efficient multigrid methods for mimetic finite difference discretizations, since it allows us to use canonical inter-grid transfer operators arising from the finite element framework. We provide special Local Fourier Analysis and numerical results to demonstrate the efficiency of such multigrid methods.