Construction of explicit extension operators on general finite element grids
Applied Numerical Mathematics
Finite elements for elliptic problems with wild coefficients
Computational science, mathematics and software
Mathematics of Computation
A variational discretization concept in control constrained optimization: the linear-quadratic case
Computational Optimization and Applications
Domain decomposition method for dynamic faulting under slip-dependent friction
Journal of Computational Physics
IPIC Domain decomposition algorithm for parabolic problems
Applied Mathematics and Computation
Some inequalities for eigenvalues of Schur complements of Hermitian matrices
Journal of Computational and Applied Mathematics
A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Multiscale finite element methods for high-contrast problems using local spectral basis functions
Journal of Computational Physics
Mathematics and Computers in Simulation
Robust Equilibrated Residual Error Estimator for Diffusion Problems: Conforming Elements
SIAM Journal on Numerical Analysis
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The purpose of this paper is to give a unified investigation of a class of nonoverlapping domain decomposition methods for solving second-order elliptic problems in two and three dimensions. The methods under scrutiny fall into two major categories: the substructuring--type methods and the Neumann--Neumann-type methods. The basic framework used for analysis is the parallel subspace correction method or additive Schwarz method, and other technical tools include local-global and global-local techniques. The analyses for both two- and three-dimensional cases are carried out simultaneously. Some internal relationships between various algorithms are observed and several new variants of the algorithms are also derived.