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Mathematics 2019, 7(2), 128; https://doi.org/10.3390/math7020128

SUPG Approximation for the Oseen Viscoelastic Fluid Flow with Stabilized Lowest-Equal Order Mixed Finite Element Method

1
School of Mathematical Sciences, East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200241, China
2
Department of Mathematics, Faculty of Science, Comilla University, Comilla 3506, Bangladesh
3
College of Science, Donghua Univeristy, Shanghai 201620, China
*
Author to whom correspondence should be addressed.
Received: 8 December 2018 / Revised: 12 January 2019 / Accepted: 22 January 2019 / Published: 28 January 2019
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Abstract

In this article, a stabilized mixed finite element (FE) method for the Oseen viscoelastic fluid flow (OVFF) obeying an Oldroyd-B type constitutive law is proposed and investigated by using the Streamline Upwind Petrov–Galerkin (SUPG) method. To find the approximate solution of velocity, pressure and stress tensor, we choose lowest-equal order FE triples P 1 - P 1 - P 1 , respectively. However, it is well known that these elements do not fulfill the i n f - s u p condition. Due to the violation of the main stability condition for mixed FE method, the system becomes unstable. To overcome this difficulty, a standard stabilization term is added in finite element variational formulation. The technique is applied herein possesses attractive features, such as parameter-free, flexible in computation and does not require any higher-order derivatives. The stability analysis and optimal error estimates are obtained. Three benchmark numerical tests are carried out to assess the stability and accuracy of the stabilized lowest-equal order feature of the OVFF. View Full-Text
Keywords: Oseen viscoelastic fluid; lowest-equal order FE (finite element); Streamline Upwind Petrov–Galerkin (SUPG); stabilized method Oseen viscoelastic fluid; lowest-equal order FE (finite element); Streamline Upwind Petrov–Galerkin (SUPG); stabilized method
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Hussain, S.; Batool, A.; Al Mahbub, M.A.; Nasu, N.J.; Yu, J. SUPG Approximation for the Oseen Viscoelastic Fluid Flow with Stabilized Lowest-Equal Order Mixed Finite Element Method. Mathematics 2019, 7, 128.

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