A design of residual error estimates for a high order BDF‐DGFE method applied to compressible flows
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[1] Eric Garnier,et al. Evaluation of some high‐order shock capturing schemes for direct numerical simulation of unsteady two‐dimensional free flows , 2000 .
[2] Ralf Hartmann,et al. A discontinuous Galerkin method for inviscid low Mach number flows , 2009, J. Comput. Phys..
[3] Ricardo H. Nochetto,et al. A posteriori error analysis for higher order dissipative methods for evolution problems , 2006, Numerische Mathematik.
[4] Vít Dolejsí,et al. Efficient solution strategy for the semi-implicit discontinuous Galerkin discretization of the Navier-Stokes equations , 2011, J. Comput. Phys..
[5] S. Rebay,et al. A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations , 1997 .
[6] J. Tinsley Oden,et al. A discontinuous hp finite element method for the Euler and Navier–Stokes equations , 1999 .
[7] Manil Suri,et al. A posteriori estimation of the linearization error for strongly monotone nonlinear operators , 2007 .
[8] Rüdiger Verfürth. A posteriori error estimates for nonlinear problems. Lr(0, T; Lrho(Omega))-error estimates for finite element discretizations of parabolic equations , 1998, Math. Comput..
[9] Stefano Giani,et al. Anisotropic hp-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. , 2001 .
[10] Igor Mozolevski,et al. Discontinuous Galerkin method for two-component liquid–gas porous media flows , 2012, Computational Geosciences.
[11] Alexandre Ern,et al. Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian , 2008 .
[12] Alessandro Colombo,et al. Agglomeration based discontinuous Galerkin discretization of the Euler and Navier-Stokes equations , 2012 .
[13] Rüdiger Verfürth,et al. A posteriori error estimates for nonlinear problems. Lr(0, T; Lrho(Omega))-error estimates for finite element discretizations of parabolic equations , 1998, Math. Comput..
[14] Rémi Abgrall,et al. Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics , 2011 .
[15] Ralf Hartmann,et al. Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation , 2005 .
[16] Rolf Rannacher,et al. An optimal control approach to a posteriori error estimation in finite element methods , 2001, Acta Numerica.
[17] Ricardo H. Nochetto,et al. A posteriori error estimates for the Crank-Nicolson method for parabolic equations , 2005, Math. Comput..
[18] R. Hartmann,et al. Symmetric Interior Penalty DG Methods for the CompressibleNavier-Stokes Equations I: Method Formulation , 2005 .
[19] Jiří Fürst. Modélisation numérique d'écoulements transsoniques avec des schémas TVD et ENO , 2001 .
[20] Christian Tenaud,et al. High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations , 2004 .
[21] Miloslav Feistauer,et al. On a robust discontinuous Galerkin technique for the solution of compressible flow , 2007, J. Comput. Phys..
[22] Ricardo H. Nochetto,et al. Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence , 2011, Numerische Mathematik.
[23] Nicolas Moës,et al. A new a posteriori error estimation for nonlinear time-dependent finite element analysis , 1998 .
[24] Y. Saad,et al. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .
[25] Vít Dolejší,et al. On the discontinuous Galerkin method for the numerical solution of the Navier–Stokes equations , 2004 .
[26] A. Ern,et al. Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems , 2011 .
[27] George Em Karniadakis,et al. Spectral/hp Methods for Viscous Compressible Flows on Unstructured 2D Meshes , 1998 .
[28] M. Giles,et al. Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality , 2002, Acta Numerica.
[29] Martin Vohralík,et al. A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers , 2010, SIAM J. Sci. Comput..
[30] Vít Dolejsí,et al. hp-DGFEM for nonlinear convection-diffusion problems , 2013, Math. Comput. Simul..
[31] Ricardo H. Nochetto,et al. A posteriori error estimation and adaptivity for degenerate parabolic problems , 2000, Math. Comput..
[32] Claus-Dieter Munz,et al. Explicit Discontinuous Galerkin methods for unsteady problems , 2012 .
[33] Chi-Wang Shu. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws , 1998 .
[34] Martin Vohralík,et al. A Framework for Robust A Posteriori Error Control in Unsteady Nonlinear Advection-Diffusion Problems , 2013, SIAM J. Numer. Anal..
[35] Jaromír Horácek,et al. Simulation of compressible viscous flow in time-dependent domains , 2013, Appl. Math. Comput..
[36] G Vijayasundaram,et al. Transonic flow simulations using an upstream centered scheme of Godunov in finite elements , 1986 .
[37] Vít Dolejší,et al. Adaptive backward difference formula–Discontinuous Galerkin finite element method for the solution of conservation laws , 2008 .
[38] Vít Dolejší,et al. A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow , 2004 .