On the impact of boundary conditions on dual consistent finite difference discretizations
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[1] Antony Jameson,et al. Aerodynamic design via control theory , 1988, J. Sci. Comput..
[2] B. Strand. Summation by parts for finite difference approximations for d/dx , 1994 .
[3] J. Nordström,et al. Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients , 2004, Journal of Scientific Computing.
[4] M. Giles,et al. Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality , 2002, Acta Numerica.
[5] Bertil Gustafsson,et al. On Error Bounds of Finite Difference Approximations to Partial Differential Equations—Temporal Behavior and Rate of Convergence , 2000, J. Sci. Comput..
[6] H. Kreiss,et al. Time-Dependent Problems and Difference Methods , 1996 .
[7] Magnus Svärd,et al. On the order of accuracy for difference approximations of initial-boundary value problems , 2006, J. Comput. Phys..
[8] D. Darmofal,et al. Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics , 2011 .
[9] Magnus Svärd,et al. A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions , 2007, J. Comput. Phys..
[10] Niles A. Pierce,et al. An Introduction to the Adjoint Approach to Design , 2000 .
[11] David Gottlieb,et al. Optimal time splitting for two- and three-dimensional navier-stokes equations with mixed derivatives , 1981 .
[12] Magnus Svärd,et al. Well-Posed Boundary Conditions for the Navier-Stokes Equations , 2005, SIAM J. Numer. Anal..
[13] Jan Nordström,et al. High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates , 2001 .
[14] Jason E. Hicken,et al. Summation-by-parts operators and high-order quadrature , 2011, J. Comput. Appl. Math..
[15] D. Venditti,et al. Adjoint error estimation and grid adaptation for functional outputs: application to quasi-one-dimensional flow , 2000 .
[16] Michael B. Giles,et al. Adjoint and defect error bounding and correction for functional estimates , 2003 .
[17] Jan Nordström,et al. Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains , 2012 .
[18] Jan Nordstroom,et al. The influence of open boundary conditions on the convergence to steady state for the Navier-Stokes equations , 1989 .
[19] Magnus Svärd,et al. On Coordinate Transformations for Summation-by-Parts Operators , 2004, J. Sci. Comput..
[20] Jan Nordström,et al. A stable and high-order accurate conjugate heat transfer problem , 2010, J. Comput. Phys..
[21] Jan Nordström,et al. Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form , 2012, J. Comput. Phys..
[22] Michael B. Giles,et al. Adjoint Recovery of Superconvergent Functionals from PDE Approximations , 2000, SIAM Rev..
[23] Jan Nordström,et al. The use of characteristic boundary conditions for the Navier-Stokes equations , 1995 .
[24] Endre Süli,et al. Adaptive error control for finite element approximations of the lift and drag coefficients in viscous flow , 1997 .
[25] Michael B. Giles,et al. Superconvergent lift estimates through adjoint error analysis , 2001 .
[26] Parviz Moin,et al. Verification of variable-density flow solvers using manufactured solutions , 2012, J. Comput. Phys..
[27] D. Gottlieb,et al. A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy , 1999 .
[28] Jason E. Hicken,et al. Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations , 2011, SIAM J. Sci. Comput..
[29] Magnus Svärd,et al. Steady-State Computations Using Summation-by-Parts Operators , 2005, J. Sci. Comput..
[30] Jan Nordstr. ERROR BOUNDED SCHEMES FOR TIME-DEPENDENT HYPERBOLIC PROBLEMS ∗ , 2007 .
[31] O. Pironneau. On optimum design in fluid mechanics , 1974 .
[32] D. Venditti,et al. Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows , 2003 .
[33] Jason E. Hicken. Output error estimation for summation-by-parts finite-difference schemes , 2012, J. Comput. Phys..
[34] Jan Nordström,et al. Conservative Finite Difference Formulations, Variable Coefficients, Energy Estimates and Artificial Dissipation , 2006, J. Sci. Comput..
[35] Ken Mattsson,et al. Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients , 2012, J. Sci. Comput..
[36] Jan Nordström,et al. Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations , 2012, J. Comput. Phys..
[37] John C. Strikwerda,et al. Initial boundary value problems for incompletely parabolic systems , 1976 .