Space-time discontinuous galerkin finite element method with dynamic grid motion for inviscid compressible flows II. efficient flux quadrature

摘要

A new and efficient quadrature rule for the flux integrals arising in the space-time discontinuous Galerkin dis- cretization of the Euler equations in a moving and deforming space-time domain is presented and analyzed. The quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme. The local trunction error of the resulting numerical discreti- zation is determined and is shown to be the same as when product Gauss quadrature rules are sued.