A fictitious Domain Method with Distributed Lagrange Multiplier for Parabolic Problems with Moving Problems

Document Type

Article

Publication Date

8-13-2016

Publication Title

Journal of Scientific Computing

Volume

70

Issue

2

First page number:

686

Last page number:

716

Abstract

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 L2, H1 and a new energy norm. On the other hand, we introduce a sub grid 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.

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