Additive Schwarz Methods for Elliptic Mortar Finite Element Problems

Overlapping Nonmatching Grid Mortar Element Methods for Elliptic Problems

In the first part of the paper, we introduce an overlapping mortar finite element method for solving two-dimensional elliptic problems discretized on overlapping nonmatching grids. We prove an optimal error bound and estimate the condition numbers of certain overlapping Schwarz preconditioned systems for the two-subdomain case. We show that the error bound is independent of the size of the over...

Additive Schwarz for Elliptic Mortar Finite

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 des...

Additive Schwarz methods for the Crouzeix-Raviart mortar finite element for elliptic problems with discontinuous coefficients

In this paper, we propose two variants of the additive Schwarz method for the approximation of second order elliptic boundary value problems with discontinuous coefficients, on nonmatching grids using the lowest order Crouzeix-Raviart element for the discretization in each subdomain. The overall discretization is based on the mortar technique for coupling nonmatching grids. The convergence beha...

A Sharpened Condition Number Estimate for the BPX Preconditioner of Elliptic Finite Element Problems on Highly Nonuniform Triangulations

In this paper it is shown that for highly nonuniformly refined triangulations the condition number of the BPX preconditioner for elliptic finite element problems grows at most linearly in the depth of refinement. This is achieved by viewing the computational available version of the BPX preconditioner as an abstract additive Schwarz method with exact solvers. AMS CLASSIFICATION: 65F10, 65F35, 6...