Abstract. 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, fi nite element approximation to the problem, based on a fi xed point algorithm, is proposed. Then, an error estimate between continuous solution and discrete one is obtained. Finally, some numerical tests are presented to confi rm the theoretical results.Mathematical subject classification: 35J, 35Q, 65N30, 76.

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, fi nite element approximation to the problem, based on a fi xed point algorithm, is proposed. Then, an error estimate between continuous solution and discrete one is obtained. Finally, some numerical tests are presented to confi rm the theoretical results.