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@MISC{,
            author = {Dolej{\v s}{\'{\i}}, V{\'{\i}}t},
          keywords = {compressible Navier-Stokes equations, discontinuous Galerkin finite element method, nonlinear},
             title = {A design of residual error estimates for a high order BDF-DGFEM applied to the compressible flows},
           journal = {International Journal for Numerical Methods in Fluids},
              year = {2013},
          abstract = {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 (BDF-DGFE) 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 BDF-DGFE discretization are solved by an iterative
Newton-like method. The main benefit of this paper are residual error estimates which 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.},
  Preprint project = {NCMM},
     Preprint year = {2013},
   Preprint number = {11},
       Preprint ID = {NCMM/2013/11}
}