On the Coupling of Local Discontinuous Galerkin and Conforming Finite Element Methods
Journal of Scientific Computing
FETI and FETI-DP Methods for Spectral and Mortar Spectral Elements: A Performance Comparison
Journal of Scientific Computing
Mathematics of Computation
A mortar approach for the analysis and optimization of composite laminated plates
Computational structures technology
The Mortar Finite Element Method for the Cardiac “Bidomain” Model of Extracellular Potential
Journal of Scientific Computing
Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes
Journal of Scientific Computing
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
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The mortar methods are based on domain decomposition and they allow for the coupling of different variational approximations in different subdomains. The resulting methods are nonconforming but still yield optimal approximations. In this paper, we will discuss iterative substructuring algorithms for the algebraic systems arising from the discretization of symmetric, second-order, elliptic equations in two dimensions. Both spectral and finite element methods, for geometrically conforming as well as nonconforming domain decompositions, are studied. In each case, we obtain a polylogarithmic bound on the condition number of the preconditioned matrix.