Mixed Variational Formulation and Numerical Analysis of Thermally Coupled Nonlinear Darcy Flows

A mixed variational formulation and its finite element approximate procedure combined with a fixed point algorithm is presented for solving a thermally coupled nonlinear Darcy flow problem. Existence and uniqueness of the solution to the nonlinear mixed variational formulation are established. A more general result on uniqueness of the continuous problem is presented. Numerical analysis of the finite element approximation 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.

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