### 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 language | English |
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Journal | Advances in Computational Mathematics |

DOIs | |

Publication status | Accepted/In press - Jan 1 2018 |

### Fingerprint

### 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

*Advances in Computational Mathematics*. https://doi.org/10.1007/s10444-018-9649-x

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

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Galerkin FEM for a time-fractional Oldroyd-B fluid problem

AU - Al-Maskari, Mariam

AU - Karaa, Samir

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Convolution quadrature

KW - Error estimate

KW - Finite element method

KW - Nonsmooth data

KW - Time-fractional Oldroyd-B fluid problem

UR - http://www.scopus.com/inward/record.url?scp=85056619264&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056619264&partnerID=8YFLogxK

U2 - 10.1007/s10444-018-9649-x

DO - 10.1007/s10444-018-9649-x

M3 - Article

AN - SCOPUS:85056619264

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

SN - 1019-7168

ER -