Finite-element solution of flow problems with trailing conditions. (English) Zbl 0766.76049

Summary: The paper deals with the finite-element solution of stream function problems describing nonviscous subsonic irrotational flows past profiles. The main emphasis is laid on the treatment of the nonstandard trailing stagnation conditions which lead to physically admissible solutions. The paper presents a general conception of stream function finite-element modelling of complicated flow problems and a complete theory of the finite-element approximations, including the investigation of the existence and uniqueness of the solution of the nonsymmetric discrete problem and the convergence of approximate solutions to the exact solution.


76M10 Finite element methods applied to problems in fluid mechanics
76G25 General aerodynamics and subsonic flows
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
Full Text: DOI


[1] Axelsson, O., Solution of linear systems of equations: Iterative methods, (Barker, V. A., Sparse Matrix Techniques, 572 (1977), Springer: Springer Berlin), Lecture Notes in Math. · Zbl 0566.65017
[2] Babus̆ka, I.; Práger, M.; Vitásek, E., Numerical Processes in Differential Equations (1966), SNTL, Prague/Wiley: SNTL, Prague/Wiley New York · Zbl 0156.16003
[3] C̆erný, I., Foundation of Analysis in the Complex Domain (1992), Academia, Prague/Ellis Horwood: Academia, Prague/Ellis Horwood Chichester
[4] Ciarlet, P. G., The Finite Element Method for Elliptic Problems, Stud. Math. Appl., 4 (1978), North-Holland: North-Holland Amsterdam · Zbl 0445.73043
[5] Ciarlet, P. G.; Raviart, P.-A., Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg., 2, 1, 17-31 (1973) · Zbl 0251.65069
[6] Ciavaldini, J. F.; Pogu, M.; Tournemine, G., Existence and regularity of stream functions for subsonic flows past profiles with a sharp trailing edge, Arch. Rational Mech. Anal., 93, 1-14 (1986) · Zbl 0621.76067
[7] Feistauer, M., Solution of elliptic problem with not fully specific Dirichlet boundary value conditions and its application in hydrodynamics, Apl. Mat., 24, 67-74 (1979) · Zbl 0399.35032
[8] Feistauer, M., Mathematical study of three-dimensional axially symmetric stream fields of an ideal fluid, (Brosowski, B.; Martensen, E., Methods and Techniques of Mathematical Physics, 21 (1981), Lang: Lang Frankfurt am Main), 45-62, Methoden Verfahren Math. Phys.
[9] Feistauer, M., Discrete Methods of the Solution of Differential Equations (1981), SPN, Prague: SPN, Prague Czech
[10] Feistauer, M., Mathematical study of rotational incompressible non-viscous flows through multiply connected domains, Apl. Mat., 26, 345-364 (1981) · Zbl 0486.76025
[11] Feistauer, M., Numerical solution of non-viscous channel flows, (Meister, E.; Nickel, K.; Polás̆ek, J., Mathematical Methods in Fluid Mechanics, 24 (1982), Lang: Lang Frankfurt am Main), 65-78, Methoden Verfahren Math. Phys.
[12] Feistauer, M., Subsonic irrotational flows in multiply connected domains, Math. Methods Appl. Sci., 4, 230-242 (1982) · Zbl 0488.76065
[13] Feistauer, M., On irrotational flows through cascades of profiles in a layer of variable thickness, Apl. Mat., 29, 423-458 (1984) · Zbl 0598.76061
[14] Feistauer, M., On the finite element approximation of a cascade flow problem, Numer. Math., 50, 655-684 (1987) · Zbl 0646.76085
[15] Feistauer, M., Nonlinear elliptic problems with incomplete Dirichlet conditions and the stream function solution of subsonic rotational flows past profiles or cascades of profiles, Apl. Mat., 34, 4, 318-339 (1989) · Zbl 0682.76055
[16] Feistauer, M.; Felcman, J.; Vlás̆ek, Z., Finite element solution of flows through cascades of profiles in a layer of variable thickness, Apl. Mat., 31, 309-339 (1986) · Zbl 0641.76067
[17] Feistauer, M.; Hunĕk, M., Solution of an axially symmetric flow by the finite element method, Stroj. C̆as., 34, 607-621 (1983), in Czech.
[18] Feistauer, M.; R̆ímánek, J., Subsonic irrotational flow of compressible fluid in axially symmetric channels, Apl. Mat., 20, 266-279 (1975) · Zbl 0323.76041
[19] Felcman, J., Numerical solution of flows in cascades of blades by the finite element method, Ph.D. Thesis (1986), Charles Univ: Charles Univ Prague, in Czech.
[20] Kufner, A.; John, O.; Fuc̆ík, S., Function Spaces (1977), Academic: Academic Prague
[21] Morton, K. W., Finite element methods for non-self-adjoint problems, (Turner, P. R., Topics in Numerical Analysis, 965 (1982), Springer: Springer Berlin), 113-148, Lecture Notes in Math. · Zbl 0551.65075
[22] Nec̆as, J., Les Méthodes Directes en Théorie des Équations Elliptiques (1967), Academia: Academia Prague/Masson, Paris · Zbl 1225.35003
[23] Rokyta, M., Numerical solution of strongly nonlinear elliptic problems, Diploma Thesis (1985), Charles Univ: Charles Univ Prague, in Czech.
[24] Varga, R. S., Matrix Iterative Analysis (1962), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0133.08602
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.