Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows

We present a new stabilized finite element method for incompressible flows based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of finite element solutions are derived for classical one-level method. Combining the techniques of two-level discretizations, we propose two-lev...

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Main Authors: Rong An, Xian Wang
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/698354
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author Rong An
Xian Wang
author_facet Rong An
Xian Wang
author_sort Rong An
collection DOAJ
description We present a new stabilized finite element method for incompressible flows based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of finite element solutions are derived for classical one-level method. Combining the techniques of two-level discretizations, we propose two-level Stokes/Oseen/Newton iteration methods corresponding to three different linearization methods and show the stability and error estimates of these three methods. We also propose a new Newton correction scheme based on the above two-level iteration methods. Finally, some numerical experiments are given to support the theoretical results and to check the efficiency of these two-level iteration methods.
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institution Kabale University
issn 1085-3375
1687-0409
language English
publishDate 2014-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-57a508b4f52a433aacf2c6752852b43a2025-02-03T05:51:44ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/698354698354Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible FlowsRong An0Xian Wang1College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaWe present a new stabilized finite element method for incompressible flows based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of finite element solutions are derived for classical one-level method. Combining the techniques of two-level discretizations, we propose two-level Stokes/Oseen/Newton iteration methods corresponding to three different linearization methods and show the stability and error estimates of these three methods. We also propose a new Newton correction scheme based on the above two-level iteration methods. Finally, some numerical experiments are given to support the theoretical results and to check the efficiency of these two-level iteration methods.http://dx.doi.org/10.1155/2014/698354
spellingShingle Rong An
Xian Wang
Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows
Abstract and Applied Analysis
title Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows
title_full Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows
title_fullStr Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows
title_full_unstemmed Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows
title_short Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows
title_sort two level brezzi pitkaranta stabilized finite element methods for the incompressible flows
url http://dx.doi.org/10.1155/2014/698354
work_keys_str_mv AT rongan twolevelbrezzipitkarantastabilizedfiniteelementmethodsfortheincompressibleflows
AT xianwang twolevelbrezzipitkarantastabilizedfiniteelementmethodsfortheincompressibleflows