Abstract
The modeling of numerous industrial processes leads to multifield problems, which are governed by the coupled interaction of several physical fields. As an example, consider electromagnetic forming, where the evolution of the deformation field of a mechanical structure consisting of well conducting material is coupled with an electromagnetic field, triggering a Lorentz force, which drives the deformation process. The purpose of the work reported on here is to develop techniques for a posteriori error control for the finite element approximation to the solution of certain systems of two boundary value problems that are coupled via their coefficients and their right-hand sides. As a first step, an error estimator for the right-hand side of the mechanical subsystem is presented in the case of a simplified model problem for the electromagnetic system. The particular influence of the mixed character of the evolution equations is discussed for a numerical example.
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Stiemer, M. (2006). Error Control for Discretizations of Electromagnetic-Mechanical Multifield Problem. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_19
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DOI: https://doi.org/10.1007/978-3-540-34288-5_19
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