On a nonoverlapping additive Schwarz method for h‐p discontinuous Galerkin discretization of elliptic problems |
| |
| Authors: | Piotr Krzy?anowski |
| |
| Affiliation: | University of Warsaw, Poland |
| |
| Abstract: | The condition number of a discontinuous Galerkin  finite element discretization preconditioned with a nonoverlapping additive Schwarz method is analyzed. We improve the result of Antonietti and Houston (J Sci Comput 46 (2011), 124–149), where a bound  has been proved for a two‐level nonoverlapping additive Schwarz method with coarse problem using polynomials of degree  on a coarse mesh size  . In a more general framework, where the concurrency of the algorithm is increased by applying solvers on subdomains smaller than the coarse grid cells, we prove that the condition number of the preconditioned system is  where  is the coarse space element degree polynomial and  is the size of subdomain where local problems are solved in parallel. Our result also extends to the case of discontinuous coefficient, piecewise constant on the coarse grid, for a composite continuous–discontinuous Galerkin discretization. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1572–1590, 2016 |
| |
| Keywords: | additive Schwarz method discontinuous Galerkin h‐p discretization |
|
|
