A very efficient preconditioner for mixed finite element approximations
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In this work, we propose an iterative scheme to solve problems arising in the context of mixed element approximation spaces. The strategy consists of using the matrix of constant boundary fluxes as a preconditioner to solve the higher-order flux problem. The latter is solved iteratively by means of a conjugate gradient scheme. In the presented numerical tests, this strategy has shown to be convergent in a few iterations for different problems in 2D and 3D. In addition, as internal fluxes are condensed, only boundary variables need to be computed. This strategy relates to the BDDC technique and can be efficiently used to develop fast multi-scale approximations in future work.
