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.

Researchers should cite this work as follows:

• Carmen Rodrigo (2016), "On the Design of a Finite Element Multigrid Solver for Mimetic Finite Difference Schemes," https://nanohub.org/resources/23476.

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1. design
2. finite difference methods
3. Finite Element Method/Analysis (FEM)
4. Illinois
5. mimetic
6. multigrid
7. NanoBio Node at Illinois
8. solver