A Fictitious Domain Method with Distributed Lagrange Multiplier for Parabolic Problems With Moving Interfaces
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In this paper, we study the fictitious domain method with distributed Lagrange multiplier for the jump-coefficient parabolic problems with moving interfaces. The equivalence between the fictitious domain weak form and the standard weak form of a parabolic interface problem is proved, and the uniform well-posedness of the full discretization of fictitious domain finite element method with distributed Lagrange multiplier is demonstrated. We further analyze the convergence properties for the fully discrete finite element approximation in the norms of \(L^2\), \(H^1\) and a new energy norm. On the other hand, we introduce a subgrid integration technique in order to allow the fictitious domain finite element method to be performed on the triangular meshes without doing any interpolation between the authentic domain and the fictitious domain. Numerical experiments confirm the theoretical results, and show the good performances of the proposed schemes.
KeywordsFictitious domain method Distributed Lagrange multiplier Fully discrete finite element scheme Subgrid integration Immersed moving interface
Mathematics Subject Classification65N30 65R20
P. Sun was partially supported by NSF Grant DMS-1418806 and UNLV Faculty Opportunity Award (2013–2015); C. Wang was supported by UNLV Faculty Opportunity Award during his visit at UNLV in 2014.
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