Unconditionally Optimal Error Estimate of a Linearized Second-Order Fully Discrete Finite Element Method for Bioconvection Flows with Concentration-Dependent Viscosity
Abstract
In this paper, the coupled and decoupled BDF2 finite element discrete schemes are obtained for the time-dependent bioconvection flows problem with concentration dependent viscosity, which consists of the Navier-Stokes equations and a linear convection-diffusion equation modeling the concentration of microorganisms in a culture fluid. The unconditionally optimal error estimate for the velocity and concentration in L²-norm are proved by using finite element approximations in space and finite differences in time. Finally, the numerical results for different viscosity are shown to support the theoretical analysis.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Nanofluid Flow and Heat Transfer
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Journal of Computational Mathematics
- Publisher
- Global Science Press
- Volume
- 45
- Issue
- 1
- Pages
- 266-293
- Publication date
- 19 August 2026
- Language
- EN