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    Anderson, Michael L. Bangerth, Wolfgang and Carey, Graham F. 2005. Analysis of parameter sensitivity and experimental design for a class of nonlinear partial differential equations. International Journal for Numerical Methods in Fluids, Vol. 48, Issue. 6, p. 583.
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Finite element error estimates for subsonic flow

  • S. S. Chow (a1) and G. F. Carey (a1)
Abstract

Error estimates are derived for a finite element analysis of plane steady subsonic flows described by the full potential equation. The analysis is based on the use of the theory of variational inequalities to accomodate the subsonic flow constraint and leads to a suboptimal estimate relative to that obtained for linear potential flow. We then consider an alternative dual formulation of the problem and obtain an optimal estimate subject to reasonable regularity assumptions.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1987
References
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[1]Bers, L., Mathematical aspects of subsonic and transonic gas dynamics (Interscience, New York, 1958).
[2]Brezis, H. and Stanipacchia, G., “The hodograph method in fluid mechanics in the light of variational inequalities”, Arch. Rational Mech. Anal. 61, 1 (1976), 1–18.
[3]Bristeau, M., Glowinski, R., Periaux, J., Perrier, P., Pirfonneau, O., and Poirier, G., “Transonic flow simulation by finite element and least square methods”, in Finite elements in fluids Vol. 4, Gallagher, R. H. et al. , (eds.) (Wiley, New York, 1982).
[4]Carey, G. F. and Pan, T. T., “Computation of subcritical compressible flows”, Computers and Fluids 9 (1981), 33–41.
[5]Carey, G. F. and Pan, T. T., “Shock free redesign using finite elements”, Comm. Appl. Num. Meth. (in press) (1985).
[6]Dinh, H. and Carey, G. F., “Approximate analysis of regularized compressible flow”, J. Nonlin. Anal. (in review) (1984).
[7]Dinh, H. and Carey, G. F., “Some results concerning approximation of regularized compressible flow”, Internal. J. Numer. Methods Fluids 5 (1985), 299–302.
[8]Falk, R. S., “Approximate solutions of some variational inequalitis with order of convergence estimates”, Ph.D. Thesis, Cornell University, Ithaca, New York, 1971.
[9]Falk, R. S. and Mercier, B., “Error estimates for elasto-plastic problems”, RAIRO Anal. Numer. 11, 2 (1977), 135–144.
[10]Finn, R. and Gilbarg, D., “Asymptotic behavior and uniqueness of plane subsonic flows”, Comm. Pure Appl. Math. 10 (1957), 23–63.
[11]Germain, P., “Ecoulements transsoniques homogènes”, 5 Prog. in aeronautical sci. (1964), 143–273.
[12]Glowinski, R., Lions, J. L. and Tremoliers, R., “Numerical analysis of variational inequalities”, (North Holland, Amsterdam, 1982).
[13]Guderley, K. G., The theory of transonic flow (Addison-Wesley, 1962) (English Translation).
[14]Hafez, M., Weilford, C., Murman, E., “Mixed finite element methods and dual iterative methods for transonic flow”, in Finite elements and fluids, Vol. 3, Gallagher, R. H. et al. , (eds.) (Wiley, New York, 1978).
[15]Li, K.-T. and Huang, A. X., “Solvability of the partial differential equation satisfied by the stream function in compressible flow and the error bound in the finite element solution”, in Finite element flow analysis, Kawai, Tadahiko (ed.) (North-Holland, Amsterdam, 1982) 387–394.
[16]Morawitz, C. S., “On the non-existence of continuous transonic flows past profiles”, Parts I, II Comm. Pure Appl. Math. 10 1957, 45–68.
[17]Shapiro, A. H., The dynamics and thermodynamics of compressible fluid flow, Vols. 1, 2. (Ronald Press, New York, 1953).
[18]Shen, S. F., “Transonic aerodynamics”, in Finite elements and fluids, Vol. 3, Gallagher, R. H. et al. , (eds.) (Wiley, New York, 1978).
[19]von Mises, R., Mathematical theory of compressible fluid flow (Academic Press, New York, 1958).
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