Finite element analysis of a coupled thermally dependent viscosity flow problem

In this work, a stationary Stokes flow with thermal effects is studied both mathematically and numerically. First, existence, uniqueness and regularity of the weak solution of the problem are established. Next, finite element approximation to the problem, based on a fixed point algorithm, is proposed. Then, an error estimate between continuous solution and discrete one is obtained. Finally, some numerical tests are presented to confirm the theoretical results.