论文标题
时间分数非线性雷利 - 斯托克斯问题的数值解决方案
Numerical solution of a time-fractional nonlinear Rayleigh-Stokes problem
论文作者
论文摘要
我们研究了具有Lipschitz连续非线性源项和初始数据$ u_0 \ in \ dot {h}^ν（ω）$，$ n in [0,2] $的半级雷利 - 斯托克斯问题问题。我们讨论解决方案的稳定性并提供规律性结果。分别基于标准的盖尔金和集结质量有限元方法分析了两种空间分离的方案。此外，通过在向后的Euler方法生成的时间上应用卷积正交来获得完全离散的方案，并得出最佳的误差估计值，以使其平滑和非平滑的初始数据。最后，提供了数值示例以说明理论结果。
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 $u_0\in\dot{H}^ν(Ω)$, $ν\in[0,2]$. 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.
