Journal of Scientific Computing
Short Note: An explicit expression for the penalty parameter of the interior penalty method
Journal of Computational Physics
Journal of Scientific Computing
BDDC methods for discontinuous Galerkin discretization of elliptic problems
Journal of Complexity
Journal of Computational and Applied Mathematics
Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations
Journal of Scientific Computing
A Class of Domain Decomposition Preconditioners for hp-Discontinuous Galerkin Finite Element Methods
Journal of Scientific Computing
Journal of Scientific Computing
Schwarz preconditioned CG algorithm for the mortar finite element
Numerical Algorithms
A BDDC algorithm for a class of staggered discontinuous Galerkin methods
Computers & Mathematics with Applications
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We present some two-level nonoverlapping and overlapping additive Schwarz methods for a discontinuous Galerkin method for solving second order elliptic problems. It is shown that the condition numbers of the preconditioned systems are of the order $O(\frac{H}{h})$ for the nonoverlapping Schwarz methods and of the order $O(\frac{H}{\delta})$ for the overlapping Schwarz methods, where h and H stand for the fine-mesh size and the coarse-mesh size, respectively, and $\delta$ denotes the size of the overlaps between subdomains. Numerical experiments are provided to gauge the efficiency of the methods and to validate the theory.