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.
Author: | Julia Niemeyer, Bernd Simeon |
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URN: | urn:nbn:de:hbz:386-kluedo-34442 |
Document Type: | Preprint |
Language of publication: | English |
Date of Publication (online): | 2013/03/07 |
Year of first Publication: | 2013 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2013/03/07 |
Tag: | FEM-FCT stabilization; partial differential-algebraic equations; positivity preserving time integration |
Page Number: | 17 |
Faculties / Organisational entities: | Kaiserslautern - 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 |