On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-by-Parts Form

In this paper we generalize results regarding the order of accuracy of finite difference operators on summation-by-parts (SBP) form, previously known to hold on uniform grids, to grids with arbitra ...

[1]  Magnus Svärd,et al.  On Coordinate Transformations for Summation-by-Parts Operators , 2004, J. Sci. Comput..

[2]  Jan Nordström,et al.  On the Suboptimal Accuracy of Summation-by-parts Schemes with Non-conforming Block Interfaces , 2016 .

[3]  B. Gustafsson The convergence rate for difference approximations to mixed initial boundary value problems , 1975 .

[4]  Magnus Svärd,et al.  Review of summation-by-parts schemes for initial-boundary-value problems , 2013, J. Comput. Phys..

[5]  H. Kreiss,et al.  Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations , 1974 .

[6]  David C. Del Rey Fernández,et al.  Corner-corrected diagonal-norm summation-by-parts operators for the first derivative with increased order of accuracy , 2017, J. Comput. Phys..

[7]  B. Strand Summation by parts for finite difference approximations for d/dx , 1994 .

[8]  Bertil Gustafsson,et al.  The convergence rate for difference approximations to general mixed initial boundary value problems , 1981 .

[9]  Bradley K. Alpert,et al.  Hybrid Gauss-Trapezoidal Quadrature Rules , 1999, SIAM J. Sci. Comput..

[10]  Jan Nordström,et al.  Conservative Finite Difference Formulations, Variable Coefficients, Energy Estimates and Artificial Dissipation , 2006, J. Sci. Comput..

[11]  J. Nordström,et al.  Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients , 2004, Journal of Scientific Computing.

[12]  Magnus Svärd,et al.  On the order of accuracy for difference approximations of initial-boundary value problems , 2006, J. Comput. Phys..

[13]  Ken Mattsson,et al.  Optimal diagonal-norm SBP operators , 2014, J. Comput. Phys..

[14]  Gregor Gassner,et al.  A Skew-Symmetric Discontinuous Galerkin Spectral Element Discretization and Its Relation to SBP-SAT Finite Difference Methods , 2013, SIAM J. Sci. Comput..

[15]  Travis C. Fisher,et al.  High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains , 2013, J. Comput. Phys..

[16]  David Gottlieb,et al.  Spectral Methods on Arbitrary Grids , 1995 .

[17]  Jan Nordström,et al.  Summation-by-Parts operators with minimal dispersion error for coarse grid flow calculations , 2017, J. Comput. Phys..

[18]  Jason E. Hicken,et al.  Summation-by-parts operators and high-order quadrature , 2011, J. Comput. Appl. Math..

[19]  Jan Nordström,et al.  Uniformly best wavenumber approximations by spatial central difference operators , 2015, J. Comput. Phys..

[20]  David C. Del Rey Fernández,et al.  A generalized framework for nodal first derivative summation-by-parts operators , 2014, J. Comput. Phys..

[21]  David C. Del Rey Fernández,et al.  Multidimensional Summation-by-Parts Operators: General Theory and Application to Simplex Elements , 2015, SIAM J. Sci. Comput..

[22]  D. Gottlieb,et al.  A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy , 1999 .

[23]  Philipp Öffner,et al.  Summation-by-parts operators for correction procedure via reconstruction , 2015, J. Comput. Phys..

[24]  Mark H. Carpenter,et al.  Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods , 2009, SIAM J. Sci. Comput..

[25]  Magnus Svärd,et al.  Response to “Convergence of Summation-by-Parts Finite Difference Methods for the Wave Equation” , 2018, J. Sci. Comput..

[26]  Gregor Gassner,et al.  Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations , 2016, J. Comput. Phys..