Department of Numerical Mathematics Faculty of Mathematics and Physics Charles University

A design of residual error estimates for a high order BDF-DGFE method applied to compressible flows

  • ID: 2658, RIV: 10159216
  • ISSN: 0271-2091, ISBN: not specified
  • source: International Journal for Numerical Methods in Fluids
  • keywords: discontinuous Galerkin finite element method; compressible Navier-Stokes equations; nonlinear algebraic problems; residual error estimates; mesh adaptation; unsteady problems
  • authors: Vít Dolejší
  • authors from KNM: Dolejší Vít


We deal with the numerical solution of the non-stationary compressible Navier-Stokes equations with the aid of the backward difference formula - discontinuous Galerkin finite element method. This scheme is sufficiently stable, efficient and accurate with respect to the space as well as time coordinates. The nonlinear algebraic systems arising from the backward difference formula - discontinuous Galerkin finite element discretization are solved by an iterative Newton-like method. The main benefit of this paper are residual error estimates that are able to identify the computational errors following from the space and time discretizations and from the inexact solution of the nonlinear algebraic systems. Thus, we propose an efficient algorithm where the algebraic, spatial and temporal errors are balanced. The computational performance of the proposed method is demonstrated by a list of numerical experiments.