2024/05/03 by Sylla, Abraham · 2 citations
#35L65 #65M08 #65M12 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2405.02203
We build a finite volume scheme for the scalar conservation law ∂t u + ∂x (H(x, u)) = 0 with bounded initial condition for a wide class of flux function H, convex with respect to the second variable. The main idea for the construction of the scheme is to use the theory of discontinuous flux. We prove that the resulting approximating sequence converges boundedly almost everywhere on \mathopen]0, +∞\mathclose[ to the entropy solution.