English

$L^\infty(L^\infty)$-boundedness of DG($p$)-solutions for nonlinear conservation laws with boundary conditions

Numerical Analysis 2026-02-04 v1

Abstract

We prove the L(L)L^\infty(L^\infty)-boundedness of a higher-order shock-capturing streamline-diffusion DG-method based on polynomials of degree p0p\geq 0 for general scalar conservation laws. The estimate is given for the case of several space dimensions and for conservation laws with initial and boundary conditions.

Keywords

Cite

@article{arxiv.1011.2750,
  title  = {$L^\infty(L^\infty)$-boundedness of DG($p$)-solutions for nonlinear conservation laws with boundary conditions},
  author = {Lutz Angermann and Christian Henke},
  journal= {arXiv preprint arXiv:1011.2750},
  year   = {2026}
}