Explicit and implicit FEM-FCT algorithms with flux linearization

Kuzmin, Dmitri

doi:10.1016/j.jcp.2008.12.011

Cited by 118 publications

(173 citation statements)

References 25 publications

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“…We select here the Finite Element Method -Flux Corrected Transport (FEM-FCT) scheme [2,1,16,17] as starting point of our work. In short, this stabilization operates directly on the algebraic level by modifying the system matrix and the right hand side vector, and it seems to produce less wriggles than most other techniques [18].…”

Section: Positivity Preserving Schemesmentioning

confidence: 99%

“…Taking the recently developed Finite Element Method -Flux Corrected Transport Scheme (FEM-FCT) [1,2] as starting point, we focus on a partial differential-algebraic framework that allows a general coupling procedure where boundary conditions are expressed as constraints and appended by means of Lagrange multipliers. The stabilization approach that we provide makes it possible to model and stabilize a flow problem as part of a more general coupled system that may stem from fluid-structure interaction, from domain decomposition or from other multiphysics models, see, e.g., [3,4,5,6,7,8] for such applications.…”

Section: Introductionmentioning

confidence: 99%

“…A different route is taken by the FEM-FCT scheme that operates directly on the system matrices derived from the standard Galerkin finite element method. This stabilization constructs first a very diffusive but non-oscillating and positivity preserving scheme and then, in a second step, corrects the diffusive low order solution by a limiting post processing based on antidiffusive terms that are computed from the standard high order solution [2,1,16,17]. The FEM-FCT scheme has been shown to produce competitive results in comparison with the other techniques [18].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On finite element method–flux corrected transport stabilization for advection–diffusion problems in a partial differential–algebraic framework

Vuong

Simeon

2014

Journal of Computational and Applied Mathematics

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An extension of the finite element method-flux corrected transport stabilization (FEM-FCT) for hyperbolic problems in the context of partial differentialalgebraic 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 differentialalgebraic equation (DAE) is shown, under a mild restriction on the time stepsize. As crucial tool in the analysis, the Drazin inverse and the corresponding Drazin ODE are explicitly derived. Numerical results are presented for nonconstant 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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Section: Positivity Preserving Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On finite element method–flux corrected transport stabilization for advection–diffusion problems in a partial differential–algebraic framework

Vuong

Simeon

2014

Journal of Computational and Applied Mathematics

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“…In the methods proposed in [22,23], f * (u k , u k−1 ) is a nonlinear term. A linear FEM-FCT scheme was presented recently in [21]. The idea of this scheme consists in replacing u k in (25) by an approximation which can be computed with an explicit scheme.…”

Section: The Equations For the Chemical Reactionmentioning

confidence: 99%

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

John

Roland

2010

Numerical Meth Engineering

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Population balance systems are models for processes in nature and industry which lead to a coupled system of equations (Navier-Stokes equations, transport equations, . . .) where the equations are defined in domains with different dimensions. This paper will study the impact of using different schemes for solving the three-dimensional equation of a precipitation process in a two-dimensional flow domain. The numerical schemes for the three-dimensional equation are assessed with respect to the median of the volume fraction of the particle size distribution and the computational costs. It turns out that in the case of a structured flow field with small variations in time all schemes give qualitatively the same results. For a highly time-dependent flow field, the evolution of the median of the volume fraction differs considerably between first order and higher order schemes.

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“…Obviously, this approach is not an option in the context of continuous finite element schemes. The discrete maximum principle for (bi-)linear approximations can be enforced, e.g., using the flux-corrected transport (FCT) algorithm [3,5]. However, its extension to higher-order finite elements is still an open problem.…”

Section: Introductionmentioning

confidence: 99%

A parameter-free smoothness indicator for high-resolution finite element schemes

Kuzmin

Schieweck

2013

Open Mathematics

Self Cite

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This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in highresolution finite element schemes. A derivative of degree ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of -adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite elements. The discrete maximum principle is enforced using a linearized flux-corrected transport algorithm. The deactivation of the flux limiter in regions of high regularity makes it possible to avoid the peak clipping effect at smooth extrema without generating spurious undershoots or overshoots elsewhere. MSC:65N30

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Explicit and implicit FEM-FCT algorithms with flux linearization

Cited by 118 publications

References 25 publications

On finite element method–flux corrected transport stabilization for advection–diffusion problems in a partial differential–algebraic framework

On finite element method–flux corrected transport stabilization for advection–diffusion problems in a partial differential–algebraic framework

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

A parameter-free smoothness indicator for high-resolution finite element schemes

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