L (L )-boundedness and convergence of DG(p) solutions for nonlinear conservation laws with boundary conditions
L (L )-boundedness and convergence of DG(p) solutions for nonlinear conservation laws with boundary conditions
We prove the L∞(L∞)-boundedness of a higher-order shock-capturing streamline-diffusion discontinuous Galerkin method based on polynomials of degree p≥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. Based on this result, convergence to the …