Error estimates for discretizations of coupled electromagnetic-mechanical problems |
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| Authors: | Marcus Stiemer |
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| Affiliation: | The study of flow behaviour in packed beds is an important part of the development of powerful and economical reactors. The considered averaged flow in the reactor channel filled with pelletes is modelled by the Brinkman-Forchheimer-extended Darcy equation. For the nonlinear problem subjected to Dirichlet boundary conditions we show existence and uniqueness (for small data) of weak solutions. The velocity profiles exhibit boundary layers which have to be resolved numerically. We present error estimates for inf-sup stable finite element pairs. In the case of fully developed flow and high Reynolds number the finite element solution can be compared to the flow profile obtained by using the method of matched asymptotic expansions. Finally, numerical simulations for flows in fixed bed and packed bed membrane reactors are discussed. |
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| Abstract: | In this note, a method is outlined to obtain a priori error estimates for the finite element discretization of coupled electromagnetic mechanical problems as arise, e.g., in electromagnetic metal forming. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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