754 research outputs found

    Robust a posteriori error estimators for mixed approximation of nearly incompressible elasticity

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    This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori error estimators for the energy norm of the finite element error are proposed and analysed. We establish upper and lower bounds for the energy error in terms of the proposed error estimators and prove that the constants in the bounds are independent of the Lam\'{e} coefficients: thus the proposed estimators are robust in the incompressible limit. Numerical results are presented that validate the theoretical estimates. The software used to generate these results is available online.Comment: 23 pages, 9 figure

    Modal Theory of Skin Effect in Single and Multiple Turn Coils

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    The skin effect in circularly symmetric structures is formulated in terms of an integral equation, which may be solved in terms of the normal modes of the corresponding integral equation eigenvalue problem. The necessary modal functions are computed numerically, using a simple discrete model of the coil. The modal series solution easily accounts for electrical excitation of the coil as for external magnetic fields. A comparison with so-called "direct" calculation methods, as well as with published experimental results, shows that the method is capable of good accuracy, while effecting substantial economies in computation
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