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On Finite Element Method–Flux Corrected Transport Stabilization for Advection-Diffusion Problems in a Partial Differential-Algebraic Framework

  • An extension of the finite element method–flux corrected transport stabilization (FEM-FCT) for hyperbolic problems in the context of partial differential- algebraic equations (PDAEs) is proposed. Given a local extremum diminishing property of the spatial discretization, the positivity preservation of the one-step θ−scheme when applied to the time integration of the resulting differential- algebraic equation (DAE) is shown, under a mild restriction on the time step- size. As crucial tool in the analysis, the Drazin inverse and the corresponding Drazin ODE are explicitly derived. Numerical results are presented for non- constant and time-dependent boundary conditions in one space dimension and for a two-dimensional advection problem where the advection proceeds skew to the mesh.

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Author:Julia Niemeyer, Bernd Simeon
URN (permanent link):urn:nbn:de:hbz:386-kluedo-34442
Document Type:Preprint
Language of publication:English
Publication Date:2013/03/07
Year of Publication:2013
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2013/03/07
Tag:FEM-FCT stabilization; partial differential-algebraic equations; positivity preserving time integration
Number of page:17
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):65-XX NUMERICAL ANALYSIS
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012