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ANALYSIS AND FINITE ELEMENT APPROXIMATION OF BIOCONVECTION FLOWS WITH CONCENTRATION DEPENDENT VISCOSITY

The problem of a stationary generalized convective flow modelling bioconvection is considered. The viscosity is assumed to be a function of the concentration of the micro-organisms. As a result the PDE system describing the bioconvection model is quasilinear. The existence and uniqueness of the weak solution of the PDE system is obtained under minimum regularity assumption on the viscosity. Numerical approximations based on the finite element method are constructed and error estimates are obtained. Numerical experiments are conducted to demonstrate the accuracy of the numerical method as well as to simulate bioconvection pattern formations based on realistic model parameters.