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Title: Numerical study of two-level additive Schwarz preconditioner for discontinuous Galerkin method solving elliptic problems (English)
Author: Hammerbauer, Tomáš
Author: Dolejší, Vít
Language: English
Journal: Programs and Algorithms of Numerical Mathematics
Volume: Proceedings of Seminar. Hejnice, June 23-28, 2024
Issue: 2024
Year:
Pages: 61-71
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Category: math
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Summary: The paper deals with the analysis and numerical study of the domain decomposition based preconditioner for algebraic systems arising from the discontinuous Galerkin (DG) discretization of the linear elliptic problems. We introduce the DG discretization of the model problem and present the spectral $hp$-bound of the corresponding linear algebraic systems. Moreover, we present the two-level additive Schwarz preconditioner together with the theoretical result related to the estimate of the condition number. Finally, we present the numerical experiments supporting the theoretical results and demonstrate the efficiency of this approach for the solution of nonlinear problems. (English)
Keyword: domain decomposition
Keyword: elliptic partial differential equation
Keyword: two-level additive Schwarz preconditioner
MSC: 65F08
MSC: 65M15
MSC: 65N15
DOI: 10.21136/panm.2024.06
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Date available: 2025-06-02T07:40:10Z
Last updated: 2025-06-05
Stable URL: http://hdl.handle.net/10338.dmlcz/703211
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