Numerical solution of a time-fractional nonlinear Rayleigh-Stokes problem

arXiv2012.02826MaRDI QIDQ6355338

Samir Karaa, Mariam Al-Maskari

Publication date: 4 December 2020

Abstract: We study a semilinear fractional-in-time Rayleigh-Stokes problem for a generalized second-grade fluid with a Lipschitz continuous nonlinear source term and initial data $u_{0}indot{H}^u(Omega)$, $uin[0,2]$. We discuss stability of solutions and provide regularity results. Two spatially semidiscrete schemes are analyzed based on standard Galerkin and lumped mass finite element methods, respectively. Further, a fully discrete scheme is obtained by applying a convolution quadrature in time generated by the backward Euler method, and optimal error estimates are derived for smooth and nonsmooth initial data. Finally, numerical examples are provided to illustrate the theoretical results.

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