scholarly journals Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems

2022 ◽  
Vol 389 ◽  
pp. 114428
Author(s):  
Dmitri Kuzmin ◽  
Hennes Hajduk ◽  
Andreas Rupp
Keyword(s):  
Hyperbolic Problems ◽  
Fully Discrete

Finite volume methods, unstructured meshes and strict stability for hyperbolic problems

2003 ◽  
Vol 45 (4) ◽  
pp. 453-473 ◽  
Author(s):  
Jan Nordström ◽  
Karl Forsberg ◽  
Carl Adamsson ◽  
Peter Eliasson
Keyword(s):  
Finite Volume ◽  
Unstructured Meshes ◽  
Finite Volume Methods ◽  
Hyperbolic Problems ◽  
Strict Stability

scholarly journals Discontinuous finite volume element method of two-dimensional unsaturated soil water movement problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fan Chen ◽  
Zhixiao Xu
Keyword(s):  
Soil Water ◽  
Finite Volume ◽  
Unsaturated Soil ◽  
Water Movement ◽  
Optimal Error Estimate ◽  
Two Dimensional ◽  
Fully Discrete ◽  
Volume Method ◽  
Movement Problem ◽  
Soil Water Movement

AbstractIn this paper, a numerical approximation method for the two-dimensional unsaturated soil water movement problem is established by using the discontinuous finite volume method. We prove the optimal error estimate for the fully discrete format. Finally, the reliability of the method is verified by numerical experiments. This method is not only simple to calculate, but also stable and reliable.

NONLINEAR ASYMPTOTICS FOR HYPERBOLIC INTERNAL WAVES OF SMALL WIDTH

2006 ◽  
Vol 03 (02) ◽  
pp. 269-295 ◽  
Author(s):  
OLIVIER GUES ◽  
JEFFREY RAUCH
Keyword(s):  
Internal Waves ◽  
Transition Layer ◽  
Layer Structure ◽  
Piecewise Smooth ◽  
Transmission Problem ◽  
Internal Layer ◽  
Smooth Transition ◽  
Hyperbolic Problems ◽  
Smooth Solutions ◽  
Small Width

Semilinear hyperbolic problems with source terms piecewise smooth and discontinuous across characteristic surfaces yield similarly piecewise smooth solutions. If the discontinuous source is replaced with a smooth transition layer, the discontinuity of the solution is replaced by a smooth internal layer. In this paper we describe how the layer structure of the solution can be computed from the layer structure of the source. The key idea is to use a transmission problem strategy for the problem with the smooth internal layer. That leads to an anastz different from the obvious candidates. The obvious candidates lead to overdetermined equations for correctors. With the transmission problem strategy we compute infinitely accurate expansions.

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