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Convergence analysis of finite element methods for H (curl; Ω)-elliptic interface problems

Hiptmair, Ralf ; Li, Jingzhi ; Zou, Jun

In: Numerische Mathematik, 2012, vol. 122, no. 3, p. 557-578

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    Titre
    • Convergence analysis of finite element methods for H (curl; Ω)-elliptic interface problems
    Auteur
    • Hiptmair, Ralf. SAM, ETH Zürich, 8092, Zurich, Switzerland
    • Li, Jingzhi. Shenzhen Institute of Advanced Technology, Shenzhen, People's Republic of China
    • Zou, Jun. Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
    Type de document
    • Postprint
    Classification
    • Informatique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:317057
    Summary
    In this article we investigate the analysis of a finite element method for solving H(curl; Ω)-elliptic interface problems in general three-dimensional polyhedral domains with smooth interfaces. The continuous problems are discretized by means of the first family of lowest order Nédélec H(curl; Ω)-conforming finite elements on a family of tetrahedral meshes which resolve the smooth interface in the sense of sufficient approximation in terms of a parameter δ that quantifies the mismatch between the smooth interface and the triangulation. Optimal error estimates in the H(curl; Ω)-norm are obtained for the first time. The analysis is based on a δ-strip argument, a new extension theorem for H 1(curl; Ω)-functions across smooth interfaces, a novel non-standard interface-aware interpolation operator, and a perturbation argument for degrees of freedom for H(curl; Ω)-conforming finite elements. Numerical tests are presented to verify the theoretical predictions and confirm the optimal order convergence of the numerical solution