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A finite element method for the Tricomi problem. (English) Zbl 0439.65096

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations
65N15 Error bounds for boundary value problems involving PDEs
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References:
[1] Aziz, A.K., Leventhal, S.: Numerical solution of the Tricomi equation by the finite element method. NOL TR 74-144 (1974)
[2] Aziz, A.K., Leventhal, S.: Numerical solutions of linear partial differential equations of elliptichyperbolic type. Numerical solution of partial differential equations, III (1975), B.E. Hubbard, (ed.), pp. 55-87. New York London: Academic Press (1976),
[3] Aziz, A.K., Schneider, M.: A new uniqueness theorem for the Frankl problem inR 2. Monatsh. Math. (in press 1980)
[4] Aziz, A.K., Schneider, M.: Uniqueness of the Frankl-Morawitz problem inR 3. University of Maryland Technical Report TR-851. SIAM J. Math. Anal. (in press, 1980)
[5] Babuska, I., Aziz, A.K.: The mathematical foundation of the finite element method with applications to partial differential equations, A.K. Aziz (ed.), pp. 5-359. New York London: Academic Press (1972)
[6] Berezanskii, J.M.: Expansions in eigenfunctions of self adjoint operators. Translation Am. Math. Soc., Providence, R.I. (1968)
[7] Bitsadze, A.V.: Equations of the mixed type. New York: MacMillan (1964) · Zbl 0111.29205
[8] Deacon, A.G., Osher, S.: A finite element method for a boundary value problem of mixed type. SIAM J. Numer. Anal.16, 756-778 (1979) · Zbl 0438.65093
[9] Lesaint, P.: Finite element methods for symmetric hyperbolic equations. Numer. Math.21, 427-455 (1973) · Zbl 0283.65061
[10] Trangenstein, J.A.: A finite element method for the Tricomi problem in the elliptic region. SIAM J. Numer. Anal.14, 1066-1077 (1977) · Zbl 0399.65079
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