scholarly journals Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics

2011 ◽  
Vol 46 (1) ◽  
pp. 498-504 ◽  
Author(s):  
François Vilar ◽  
Pierre-Henri Maire ◽  
Rémi Abgrall
Keyword(s):  
Conservation Laws ◽  
Discontinuous Galerkin ◽  
Unstructured Grids ◽  
Two Dimensional ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Lagrangian Hydrodynamics ◽  
Scalar Conservation

One-Dimensional Scalar Conservation Laws with Regulated Data

2020 ◽  
Vol 52 (3) ◽  
pp. 3114-3130
Author(s):  
Helge Kristian Jenssen ◽  
Johanna Ridder
Keyword(s):  
Conservation Laws ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Scalar Conservation

scholarly journals Fractional BV spaces and applications to scalar conservation laws

2014 ◽  
Vol 11 (04) ◽  
pp. 655-677 ◽  
Author(s):  
C. Bourdarias ◽  
M. Gisclon ◽  
S. Junca
Keyword(s):  
Conservation Laws ◽  
Stability Result ◽  
Entropy Solutions ◽  
Smoothing Effect ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Regular Functions ◽  
Bv Functions ◽  
Scalar Conservation ◽  
First Time

We obtain new fine properties of entropy solutions to scalar nonlinear conservation laws. For this purpose, we study the "fractional BV spaces" denoted by BVs(ℝ) (for 0 < s ≤ 1), which were introduced by Love and Young in 1937 and closely related to the critical Sobolev space Ws,1/s(ℝ). We investigate these spaces in connection with one-dimensional scalar conservation laws. The BVs spaces allow one to work with less regular functions than BV functions and appear to be more natural in this context. We obtain a stability result for entropy solutions with BVs initial data. Furthermore, for the first time, we get the maximal Ws,p smoothing effect conjectured by Lions, Perthame and Tadmor for all nonlinear (possibly degenerate) convex fluxes.

Sign in / Sign up

Export Citation Format

Share Document