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

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

2010-11-11

arxiv.org/abs/1011.2750v1

Mathematics

Numerical Analysis

Scientific paper

We prove the $L^\infty(L^\infty)$-boundedness of a higher-order
shock-capturing streamline-diffusion DG-method based on polynomials of degree
$p\geq 0$ 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.

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