Solution of time-dependent convection-diffusion equations with the aid of higher order adaptive methods with respect to space and time
Kůs, Pavel, Dolejší, Vít
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Kůs, Pavel, Dolejší, Vít
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Gabriel R. Barrenechea, Volker John, Petr Knobloch (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates...
Martine Marion, Adeline Mollard (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem. ...
O. Axelsson (1984)
Banach Center Publications
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Christophe Buet, Stéphane Cordier, Brigitte Lucquin-Desreux, Simona Mancini (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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This paper deals with the diffusion limit of a kinetic equation where the collisions are modeled by a Lorentz type operator. The main aim is to construct a discrete scheme to approximate this equation which gives for any value of the Knudsen number, and in particular at the diffusive limit, the right discrete diffusion equation with the same value of the diffusion coefficient as in the continuous case. We are also naturally interested with a discretization which can be used with few...
Vlasák, Miloslav, Kučera, Václav
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We deal with a nonstationary semilinear singularly perturbed convection–diffusion problem. We discretize this problem by discontinuous Galerkin method in space and by midpoint rule in time. We present diffusion–uniform error estimates with sketches of proofs.
R.E. Bank, J.F. Bürgler, ... (1990/91)
Numerische Mathematik
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