Stability of finite volume approximations for the Laplacian operator on quadrilateral and triangular grids

Applied Numerical Mathematics

Volumn 51, Issue 1, 2004, Pages 101-125

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

^a UPPSALA UNIVERSITY   (Sweden)

^b SWEDISH DEFENCE RESEARCH AGENCY   (Sweden)

Author keywords

Accuracy; Finite volume methods; Stability; Unstructured grids

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; COMPUTATIONAL FLUID DYNAMICS; FINITE VOLUME METHOD; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; PROBLEM SOLVING;

SIMULTANEOUS APPROXIMATION TERM TECHNIQUE (SAT); SUMMATION-BY-PART OPERATORS (SBP); UNSTRUCTURED GRIDS;

MATHEMATICAL OPERATORS;

EID: 4344607852     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.02.001     Document Type: Article

References (22)

1. Haselbacher A., McGuirk J.J., Page G.J. Finite volume discretization aspects for viscous flows on mixed unstructured grids. AIAA J. 37:(2):1999.
2. D.J. Mavriplis, V. Venkatakrishnan, A unified multigrid solver for the Navier-Stokes equations on mixed element meshes, Technical Report, ICASE Report 95-33, NASA, Hampton, VA, 1995.
3. Mavriplis D.J. Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes. J. Comput. Phys. 145:1998.
4. D.J. Mavriplis, D.W. Levy, Transonic drag prediction using an unstructured multigrid solver, Technical Report, ICASE Report, NASA, Hampton, VA, 2002.
5. Mavriplis D.J. Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes. AIAA J. 28:(2):1990.
6. Nordström J., Forsberg K., Adamsson C., Eliasson P. Finite volume methods, unstructured meshes and strict stability for hyperbolic problems. Appl. Numer. Math. 45:2003.
7. T. Gerhold, O. Friedrich, J. Evans, Calculation of complex three-dimensional configurations employing the DLR- τ -Code, AIAA Paper 97-0167, 1997.
8. Weiss J.M., Maruszewski J.P., Smith W.A. Implicit solution of preconditioned Navier-Stokes equations using algebraic multigrid. AIAA J. 37:(1):1999.
9. Lax P.D., Richtmyer R.D. Survey of the stability of linear finite difference equations. Comm. Pure Appl. Math. 9:1956.
10. Eymard R., Gallouët T., Herbin R. Finite volume methods. Handbook of Numerical Analysis. vol. VII:2000;North-Holland, Amsterdam.
11. Kreiss H.-O., 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.
12. H.-O. Kreiss, G. Scherer, On the existence of energy estimates for difference approximations for hyperbolic systems, Technical Report, Dept. of Scientific Computing, Uppsala University, Uppsala, 1977.
13. Carpenter M.H., Gottlieb D., Abarbanel S. The stability of numerical boundary treatments for compact high-order finite difference schemes. J. Comput. Phys. 108:(2):1994.
14. Carpenter M.H., Nordström J., Gottlieb D. A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148:1999.
15. Nordström J., 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.
16. Nordström J., Carpenter M.H. High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates. J. Comput. Phys. 173:2001.
17. Kreiss H.O., Wu L. On the stability definition of difference approximations for the initial boundary value problem. Appl. Numer. Math. 1993.
18. Gustafsson B. The convergence rate for difference approximations to mixed initial boundary value problems. Math. Comp. 29:(130):1975;396-406.
19. Gustafsson B. The convergence rate for difference approximations to general mixed initial boundary value problems. SIAM J. Numer. Anal. 18:(2):1981;179-190.
20. Horn R.A., Johnson C.R. Matrix Analysis. 1990;Cambridge University Press, Cambridge.
21. Hairer E., Nørsett S.P., Wanner G. Solving Ordinary Differential Equations I. 1993;Springer, Berlin.
22. Gustafsson B., Kreiss H.-O., Oliger J. Time Dependent Problems and Difference Methods. 1995;Wiley, New York.