Fast solvers for the symmetric ipdg discretization of second order elliptic problems
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AbstractIn this paper, we develop and analyze a preconditioning technique and an iterative solver for the linear systems resulting from the discretization of second order elliptic problems by the symmetric interior penalty discontinuous Galerkin methods. The main ingredient of our approach is a stable decomposition of the piecewise polynomial discontinuous finite element space of arbitrary order into a linear conforming space and a space containing high frequency components. To derive such decomposition, we introduce a novel interpolation operator which projects piece-wise polynomials of arbitrary order to continuous piecewise linear functions. We prove that this operator is stable which allows us to derive the required space decomposition easily. Moreover, we prove that both the condition number of the preconditioned system and the convergent rate of the iterative method are independent of the mesh size. Numerical experiments are also shown to confirm these theoretical results.
All Author(s) ListZhong L., Chung E.T., Liu C.
Journal nameInternational Journal of Numerical Analysis and Modeling
Year2015
Month1
Day1
Volume Number12
Issue Number3
PublisherInstitute for Scientific Computing and Information
Place of PublicationCanada
Pages455 - 475
ISSN1705-5105
LanguagesEnglish-United Kingdom
KeywordsDiscontinuous galerkin methods, Iterative method, Preconditioner

Last updated on 2020-05-09 at 02:32