Galerkin FEM for a time-fractional Oldroyd-B fluid problem

Mariam Al-Maskari, Samir Karaa

Research output: Contribution to journalArticle

Abstract

We consider the numerical approximation of a generalized fractional Oldroyd-B fluid problem involving two Riemann-Liouville fractional derivatives in time. We establish regularity results for the exact solution which play an important role in the error analysis. A semidiscrete scheme based on the piecewise linear Galerkin finite element method in space is analyzed, and optimal with respect to the data regularity error estimates are established. Further, two fully discrete schemes based on convolution quadrature in time generated by the backward Euler and the second-order backward difference methods are investigated and related error estimates for smooth and nonsmooth data are derived. Numerical experiments are performed with different values of the problem parameters to illustrate the efficiency of the method and confirm the theoretical results.

Original languageEnglish
JournalAdvances in Computational Mathematics
DOIs
Publication statusAccepted/In press - Jan 1 2018

Fingerprint

Oldroyd-B Fluid
Galerkin
Error Estimates
Fractional
Regularity
Riemann-Liouville Fractional Derivative
Finite element method
Galerkin Finite Element Method
Fluids
Numerical Approximation
Convolution
Error Analysis
Quadrature
Piecewise Linear
Error analysis
Difference Method
Euler
Exact Solution
Numerical Experiment
Derivatives

Keywords

  • Convolution quadrature
  • Error estimate
  • Finite element method
  • Nonsmooth data
  • Time-fractional Oldroyd-B fluid problem

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Galerkin FEM for a time-fractional Oldroyd-B fluid problem. / Al-Maskari, Mariam; Karaa, Samir.

In: Advances in Computational Mathematics, 01.01.2018.

Research output: Contribution to journalArticle

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