Convergence analysis of finite element approximations of the Joule heating problem in three spatial dimensions
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- Holst, M.J., Larson, M.G., Målqvist, A. et al. Bit Numer Math (2010) 50: 781. doi:10.1007/s10543-010-0287-z
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In this paper we present a finite element discretization of the Joule-heating problem. We prove existence of solution to the discrete formulation and strong convergence of the finite element solution to the weak solution, up to a sub-sequence. We also present numerical examples in three spatial dimensions. The first example demonstrates the convergence of the method in the second example we consider an engineering application.