A decoupled Crank-Nicolson leap-frog scheme for the unsteady bioconvection flows problem with concentration dependent viscosity
Numerical Analysis
2025-10-17 v1 Numerical Analysis
Abstract
A fully discrete Crank--Nicolson Leap--Frog (CNLF) scheme is proposed and analyzed for the unsteady bioconvection flow problem with concentration-dependent viscosity. Spatial discretization is handled via the Galerkin finite element method (FEM), while temporal discretization employs the CNLF method for the linear terms and a semi-implicit approach for the nonlinear terms. The scheme is proven to be unconditionally stable, i.e., the time step is not subject to a restrictive upper bound. Using the energy method, -optimal error estimates are derived for the velocity and concentration . Finally, numerical experiments are presented to validate the theoretical results.
Keywords
Cite
@article{arxiv.2510.14034,
title = {A decoupled Crank-Nicolson leap-frog scheme for the unsteady bioconvection flows problem with concentration dependent viscosity},
author = {Chenyang Li},
journal= {arXiv preprint arXiv:2510.14034},
year = {2025}
}