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Literatur
AUBIN, J.P.: Approximation of Elliptic Boundary-Value Problems. John Wiley, New York (1972)
BATSCHELET, E.: Über die numerische Auflösung von Randwertproblemen bei elliptischen partiellen Differentialgleichungen. Z. Angew. Math. Phys. 3, 165–193 (1952)
BRAMBLE, J.H. and HUBBARD, B.E.: Approximation of Solutions of Mixed Boundary Value Problems for Poisson's Equation by Finite Differences. JACM 12, 114–123 (1965)
CIARLET, P.G. and RAVIART, P.-A.: Maximum Principle and Uniform Convergence for the Finite Element Method. Comp. Meth. Appl. Mech. Engin. 2, 17–31 (1973)
CIARLET, P.G., SCHULTZ, M.H. and VARGA, R.S.: Numerical Methods of High-Order Accuracy for Nonlinear Boundary Value Problems. V. Monotone Operator Theory. Num. Math. 13, 51–77 (1969)
CONCUS, P.: Static menisci in a vertical right circular cylinder. J. Fluid Mech. 34, 481–495 (1968)
COURANT, R.: Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc. 49, 1–23 (1943)
DANIEL, J.W.: The Approximate Minimization of Functionals. Prentice Hall, Inc., Englewood Cliffs, N.J. (1971)
FREHSE, J.: Morrey space methods in the theory of elliptic difference equations. Lecture Notes 333, Springer-Verlag, Berlin (1973)
FRIEDRICHS, K.O. and KELLER, H.B.: A Finite Difference Scheme for Generalized Neumann Problems, in "Numerical Solution of Partial Differential Equations", ed. J.H. Bramble. Academic Press, New York and London (1966)
GERSCHGORIN, S.: Fehlerabschätzung für das Differenzenverfahren zur Lösung partieller Differentialgleichungen. ZAMM 10, 373–382 (1930)
HERBOLD, R.J. and VARGA, R.S.: The Effect of Quadrature Errors in the Numerical Solution of Two-Dimensional Boundary Value Problems by Variational Techniques. Aeq. Math. 7, 36–58 (1971)
McALLISTER, G.T.: Mixed Boundary Value Problems for some Linear and Nonlinear Elliptic Difference Equations. J. Inst. Math. Appl. 9, 205–217 (1972)
MITTELMANN, H.D.: Die Approximation der Lösungen gemischter Randwertprobleme quasilinearer elliptischer Differentialgleichungen. preprint no. 114, Techn. Hochschule Darmstadt (1974).Eingereicht bei Computing.
OGANESJAN, L.A.: Convergence of variational difference schemes under improved approximation to the boundary. Sov. Math. Dokl. 7, 1146–1150 (1967)
ORTEGA, J.M. and RHEINBOLDT, W.C.: Iterative Solution of nonlinear equations in several variables. Academic Press, New York and London (1970)
REID, J.K.: On the Construction and Convergence of a Finite-Element Solution of Laplace's Equation. J. Inst. Math. Appl. 9, 1–13 (1972)
SCHECHTER, S.: Iteration methods for nonlinear problems. Trans. Amer. Math. Soc. 104, 179–189 (1962)
STEPLEMAN, R.S.: Finite-Dimensional Analogues of variational problems in the plane. SIAM J. Num. Anal. 8, 11–23 (1971)
STRANG, G. and FIX, G.J.: An Analysis of the Finite Element Method. Prentice Hall, Inc., Englewood Cliffs, N.J. (1973)
STUMMEL, F.: Discrete Convergence of Mappings. Proc. Conf. Num. Anal., Dublin (1972)
THOMEE, V.: Polygonal Domain Approximation in Dirichlet's Problem. J. Inst. Math. Appl. 11, 33–44 (1973)
THURAISAMY, V.: Approximate solutions for mixed boundary value problems by finite-difference methods. Math. Comp. 23, 373–386 (1969)
THURAISAMY, V.: Monotone Type Discrete Analogue for the Mixed Boundary Value Problem. Math. Comp. 23, 387–394 (1969)
TÖRNIG, W. und MEIS, Th.: Diskretisierung des Dirichletproblems nichtlinearer elliptischer Differentialgleichungen, in B. Brosowski und E. Martensen: Meth. u. Verf. d. math. Phys. Bd. 8, Bibl. Inst., Mannheim (1973)
ZLAMAL, M.: On the Finite Element Method. Num. Math. 12, 394–409 (1968)
ZLAMAL, M.: On some Finite Element Procedures for Solving Second Order Boundary Value Problems. Num. Math. 14, 42–48 (1969)
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Mittelmann, H.D. (1974). Finite — Element Verfahren bei quasi-linearen elliptischen randwertproblemen. In: Ansorge, R., Törnig, W. (eds) Numerische Behandlung nichtlinearer Integrodifferential-und Differentialgleichungen. Lecture Notes in Mathematics, vol 395. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060672
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DOI: https://doi.org/10.1007/BFb0060672
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