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

Shahid Hussain, Afshan Batool, Md. Abdullah Al Mahbub, Nasrin Jahan Nasu and Jiaping Yu
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Shahid Hussain: School of Mathematical Sciences, East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200241, China
Afshan Batool: School of Mathematical Sciences, East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200241, China
Md. Abdullah Al Mahbub: School of Mathematical Sciences, East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200241, China
Nasrin Jahan Nasu: School of Mathematical Sciences, East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200241, China
Jiaping Yu: College of Science, Donghua Univeristy, Shanghai 201620, China

Mathematics, 2019, vol. 7, issue 2, 1-19

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.

Keywords: Oseen viscoelastic fluid; lowest-equal order FE (finite element); Streamline Upwind Petrov–Galerkin (SUPG); stabilized method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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