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.
Cite this work
Researchers should cite this work as follows: