Effect of errors in the spatial geometry for temperature dependent Stokes flow
Review articleOpen access

AbstractA priori bounds are established for the solution to the problem of Stokes flow in a bounded domain, for a viscous, heat conducting, incompressible fluid, when changes in the spatial geometry are admitted. These bounds demonstrate how the velocity field and the temperature field depend on changes in the spatial geometry and also yield a convergence theorem in terms of boundary perturbations. The results have a direct bearing on an error analysis for a numerical approximation to non-isothermal Stokes flow when the boundary of a complicated domain is approximated by a simpler one, e.g., in the procedure of triangulation combined with finite elements.

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