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Volume 11, Issue 1
Analysis and Finite Element Approximation of Bioconvection Flows with Concentration Dependent Viscosity

Y. Cao & S. Chen

Int. J. Numer. Anal. Mod., 11 (2014), pp. 86-101.

Published online: 2014-11

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  • Abstract

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.

  • Keywords

bio-convection, nonlinear partial differential equations, finite element method.

  • AMS Subject Headings

35, 65N30, 92

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-86, author = {Y. Cao and S. Chen}, title = {Analysis and Finite Element Approximation of Bioconvection Flows with Concentration Dependent Viscosity}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {1}, pages = {86--101}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/515.html} }
TY - JOUR T1 - Analysis and Finite Element Approximation of Bioconvection Flows with Concentration Dependent Viscosity AU - Y. Cao & S. Chen JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 86 EP - 101 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/515.html KW - bio-convection, nonlinear partial differential equations, finite element method. AB -

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.

Y. Cao and S. Chen. (2014). Analysis and Finite Element Approximation of Bioconvection Flows with Concentration Dependent Viscosity. International Journal of Numerical Analysis and Modeling. 11 (1). 86-101. doi:
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