Variational formulation and finite element analysis of thermally coupled nonlinear flows

Title: Variational formulation and finite element analysis of thermally coupled nonlinear flows

 

Speaker: Jiang Zhu National Laboratory for Scientific Computing,Ministry of Science, Technology and Innovation, Brazil

 

Date: 16:00-17:00pm, December 11, 2013

 

Place: Conference Room B203, Department of Mathematical Sciences

 

Abstract: In this talk,  a class of nonlinear coupled models, such as thermistor problem, thermally coupled nonlinear Darcy or Hele-Shaw flows, thermally coupled Newtonian and non-Newtonian flows, coupled turbulent fluids, semiconductor device equations with Joule heating and Maxwell equations with heating are introduced firstly. Then the thermally coupled nonlinear Darcy flow is considered particularly, both classic and mixed variational formulations and their finite element approximations combined with fixed point algorithm are presented. Existence and uniqueness of the solutions are established. Finite element analysis with the corresponding error estimates is given. Numerical results are presented confirming the expected rates of convergence and illustrating the influence of the exponent of the nonlinear power law constitutive equation.

 

ContactJinxing Xie