Convergence analysis of finite element approximations of the Joule heating problem in three spatial dimensions
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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.
KeywordsFinite element methods Joule heating problem Convergence analysis
Mathematics Subject Classification (2000)65N30 35J60
- 1.Adams, R.A.: Sobolev Spaces. Academic Press, San Diego (1978) Google Scholar
- 10.Holst, M.J., Tsogtgerel, G., Zhu, Y.: Local convergence of adaptive methods for nonlinear partial differential equations. arXiv:1001.1382v1
- 13.Sun-Sig, B.: Elliptic equations with BMO coefficients in Lipschitz domains. Trans. Am. Math. Soc. 357(3), 1025–1046 (2004) Google Scholar