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

Author

Listed:
  • 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
    Department of Mathematics, Faculty of Science, Comilla University, Comilla 3506, Bangladesh)

  • 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)

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.

Suggested Citation

  • Shahid Hussain & Afshan Batool & Md. Abdullah Al Mahbub & Nasrin Jahan Nasu & Jiaping Yu, 2019. "SUPG Approximation for the Oseen Viscoelastic Fluid Flow with Stabilized Lowest-Equal Order Mixed Finite Element Method," Mathematics, MDPI, vol. 7(2), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:128-:d:201411
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