Carmen Rodrigo
On the design of a finite element multigrid solver for mimetic finite difference schemes

Applied Mathematics Department
University of Zaragoza
Spain
carmenr@unizar.es
Francisco J. Gaspar
Xiaozhe Hu
Ludmil Zikatanov

The focus of this work is to study the relation between mimetic finite difference schemes on triangular grids and some finite element methods for two model problems based on curl-rot and grad-div operators. With this purpose, modified Nédélec and Raviart-Thomas finite element methods are derived respectively. This connection allows us to design an efficient multigrid method for the curl-rot problem, by considering canonical inter-grid transfer operators arising from the finite element framework. The resulting algorithm is shown to be very robust and efficient, as confirmed by an special local Fourier analysis for edge-based discretizations on triangular grids.