Domain Decomposition Capabilities for the Mortar Finite Volume Element Methods

Since the introduction of the mortar method as a coupling technique between the spectral and nite element methods see e g it has become the most important technique in domain decomposition methods for non matching grids The active research by the scienti c computation community in this eld is motivated by its exibility and great potential for large scale parallel compu tation see e g A good description of the mortar element method can be found in The nonconforming nite element mortar method has been studied in where optimal order convergence in H norm was demonstrated Three dimensional mortar nite element analysis has been given in Non mortar mixed nite element approximations for second order elliptic problems have been discussed in The above mentioned mortar elements are de ned on non matching grids with non overlapping subdomains Recently the overlapping mortar linear nite element method was studied in where several additive Schwarz precon ditioners have been proposed and analyzed and extensive numerical examples to support the theoretical results have been reported To the authors best knowledge there has not been a study for the mortar nite volume element method In the past years the nite control volume method has drawn serious attension both form mathematicians engineers and physicists as an attractive solution technique for various applied problems see e g Following the notations and the approach of Ben Belgacem we