On the order of accuracy for difference approximations of initial-boundary value problems

Journal of Computational Physics

Volumn 218, Issue 1, 2006, Pages 333-352

  Svärd, Magnus ^a,b   Nordström, Jan ^b,c  

^a STANFORD UNIVERSITY   (United States)

^b UPPSALA UNIVERSITY   (Sweden)

^c SWEDISH DEFENCE RESEARCH AGENCY   (Sweden)

Author keywords

Boundary closure; Boundary conditions; Finite difference methods; Navier Stokes equations; Order of accuracy; Parabolic partial differential equations; Stability; Summation by parts

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; INITIAL VALUE PROBLEMS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; VISCOUS FLOW;

BOUNDARY CLOSURE; FINITE DIFFERENCE APPROXIMATIONS; FINITE-DIFFERENCE METHODS; INITIAL-BOUNDARY VALUE PROBLEMS; NAVIER-STOKES EQUATION; ORDER OF ACCURACY; PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS; POINT WISE; SECOND DERIVATIVES; SUMMATION BY PARTS;

NAVIER STOKES EQUATIONS;

EID: 33748544239     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.02.014     Document Type: Article

References (18)

1. Gustafsson B. The convergence rate for difference approximations to mixed initial boundary value problems. Math. Comp. 29 130 (1975) 396-406
2. Gustafsson B. The convergence rate for difference approximations to general mixed initial boundary value problems. SIAM J. Numer. Anal. 18 2 (1981) 179-190
3. Abarbanel S., Ditkowski A., and Gustafsson B. On error bounds of finite difference approximations to partial differential equations - temporal behavior and rate of convergence. J. Sci. Comput. (2000)
4. Mattsson K., and Nordström J. Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys. 199 2 (2004)
5. Gustafsson B., Kreiss H.-O., and Oliger J. Time Dependent Problems and Difference Methods (1995), Wiley, New York
6. Horn R.A., and Johnson C.R. Matrix Analysis (1990), Cambridge University Press, Cambridge
7. Kreiss H.-O., and Scherer G. Finite element and finite difference methods for hyperbolic partial differential equations. Mathematical Aspects of Finite Elements in Partial Differential Equations (1974), Academic Press, New York
8. H.-O. Kreiss, G. Scherer, On the existence of energy estimates for difference approximations for hyperbolic systems, Technical Report, Department of Scientific Computing, Uppsala University, 1977.
9. Strand B. Summation by parts for finite difference approximations for d/dx. J. Comput. Phys. 110 (1994)
10. Carpenter M.H., Gottlieb D., and Abarbanel S. Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes. J. Comput. Phys. 111 2 (1994)
11. Carpenter M.H., Nordström J., and Gottlieb D. A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148 (1999)
12. Nordström J., and Carpenter M.H. Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier-Stokes equations. J. Comput. Phys. 148 (1999)
13. Nordström J., and Carpenter M.H. High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates. J. Comput. Phys. 173 (2001)
14. Mattsson K., Svärd M., and Nordström J. Stable and accurate artificial dissipation. J. Sci. Comput. 21 1 (2004)
15. K. Mattsson, M. Svärd, J. Nordström, M.H. Carpenter, Accuracy requirements for transient aerodynamics, AIAA paper 2003-3689, 2003.
16. Svärd M. On coordinate transformation for summation-by-parts operators. J. Sci. Comput. 20 1 (2004)
17. Magnus Svärd, Jan Nordström, On the order of accuracy for difference approximations of initial-boundary value problems, Technical Report 2004-040, Department of Information Technology, Uppsala University, 2004.
18. Kennedy C.A., Carpenter M.H., and Lewis R.M. Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations. Appl. Numer. Math. 35 (2000)