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Implementation of the FEM-FCT method for nonstationary convection-diffusion equations
Stará, Lenka ; Knobloch, Petr (advisor) ; Dolejší, Vít (referee)
The aim of this work is the implementation and the testing of the fi- nite element method flux corrected transport (FEM-FCT) for an evolutionary convection-diffusion-reaction equation with small diffusion parameter. The basic idea of this method lies in modification of algebraic equation which is obtained from the Galerkin finite element method in order to suppress spurious oscillations and not to smear the solution considerably. In the first section of this work we in- troduce the problem of solving a convection-diffusion-reaction equation. The next section is devoted to a short introduction of the finite element method and we pro- vide the Galerkin finite element formulation of the convection-diffusion-reaction problem. Afterward we derive formulae, which are necessary for implementation FEM-FCT method. In the last section we present numerical results, which are studied at body rotation problem. 1
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The Gibbs phenomenon in the discontinuous Galerkin method
Stará, Lenka ; Kučera, Václav (advisor) ; Sváček, Petr (referee)
The solution of the Burgers' equation computed by the standard finite element method is degraded by oscillations, which are the manifestation of the Gibbs phenomenon. In this work we study the following numerical me- thods: Discontinuous Galerkin method, stable low order schemes and the flux corrected technique method in order to prevent the undesired Gibbs phenomenon. The focus is on the reduction of severe overshoots and under- shoots and the preservation of the smoothness of the solution. We consider a simple 1D problem on the interval (0, 1) with different initial conditions to demonstrate the properties of the presented methods. The numerical results of individual methods are provided. 1
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Implementation of the FEM-FCT method for nonstationary convection-diffusion equations
Stará, Lenka ; Knobloch, Petr (advisor) ; Dolejší, Vít (referee)
The aim of this work is the implementation and the testing of the fi- nite element method flux corrected transport (FEM-FCT) for an evolutionary convection-diffusion-reaction equation with small diffusion parameter. The basic idea of this method lies in modification of algebraic equation which is obtained from the Galerkin finite element method in order to suppress spurious oscillations and not to smear the solution considerably. In the first section of this work we in- troduce the problem of solving a convection-diffusion-reaction equation. The next section is devoted to a short introduction of the finite element method and we pro- vide the Galerkin finite element formulation of the convection-diffusion-reaction problem. Afterward we derive formulae, which are necessary for implementation FEM-FCT method. In the last section we present numerical results, which are studied at body rotation problem. 1
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Vegetation carbon-stores and net primary in upper Stropnice river catchment
Stará, Lenka ; Bodlák, L. ; Pokorný, J. ; Macků, J. ; Janderková, J. ; Šefrna, L. ; Středa, T. ; Burešová, Renata ; Pechar, Libor ; Cudlín, Pavel
Vegetation carbon-stores were quantified and net primary production estimated in upper Stropnice river catchment.Subsequently carbon cycle in the studied territory was composed for to estimate the total carbon balance of the area.Based on the results studied territory appear to be a carbon sink,i.e.carbon storing area.
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