×

zbMATH — the first resource for mathematics

Lineare Spline-Funktionen und die Methoden von Ritz für elliptische Randwertprobleme. (German) Zbl 0192.44503

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Agmon, S., Lectures on Elliptic Boundary Value Problems. Princeton: Van Nostrand, 1965. · Zbl 0142.37401
[2] Birkhoff, G., M.H. Schultz, & R.S. Varga, Piecewise hermite interpolation in one and two variables with applications to partial differential equations. Numer. Math. 11, 232–256 (1968). · Zbl 0159.20904 · doi:10.1007/BF02161845
[3] Bramble, J.H., & B.E. Hubbard, A priori bounds on the discretization error in the numerical solution of the Dirichlet problem. Contributions to Differential Equations 2, 229–252 (1963). · Zbl 0196.50801
[4] Bramble, J.H., & B.E. Hubbard, A theorem on error estimation for finite difference analogues of the Dirichlet problem for elliptic equations. Contributions to Differential Equations 2, 319–340 (1963). · Zbl 0196.50901
[5] Bramble, J. H., & B. E. Hubbard, Approximation of solutions of mixed boundary value problems for Poisson’s equation by finite differences. J. Association for Computing Machinery 12, 114–123 (1965). · Zbl 0125.07305 · doi:10.1145/321250.321260
[6] Bramble, J. H., & L. E. Payne, Bounds for solutions of second-order elliptic partial differential equations. Contributions to Differential Equations 1, 95–127 (1963). · Zbl 0141.09801
[7] Bramble, J. H., R. B. Kellogg, & V. Thomée, On the rate of convergence of some difference schemes for second order elliptic equations. Technical Note BN-534, Inst. for Fluid Dynamics and Appl. Math., University of Maryland, 1968.
[8] Céa, J., Approximation variationnelle des problèmes aux limites. Ann. Inst. Fourier, 14, 345–444 (1964). · Zbl 0127.08003 · doi:10.5802/aif.181
[9] Courant, R., Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc. 49, 1–23 (1943). · Zbl 0063.00985 · doi:10.1090/S0002-9904-1943-07818-4
[10] Demjanovic, Ju. K., The net method for some problems in mathematical physics. Dokl. Akad. Nauk SSSR 159 (1964); Soviet Math. 5, 1452–1456 (1964). · Zbl 0141.09903
[11] Demjanovic, Ju. K., Approximation and convergence of the net method in elliptic problems. Dokl. Akad. Nauk SSSR 170 (1966); Soviet Math. 7, 1129–1133 (1966).
[12] Fix, G., Higher-order Rayleigh-Ritz approximations. J. Math. Mech. 18, 645–657 (1969). · Zbl 0234.65095
[13] Friedrichs, K. O., & H. B. Keller, A Finite Difference Scheme for Generalized Neumann Problems. In: Numerical Solution of Partial Differential Equations. New York: Academic Press 1966, S. 1–19.
[14] Helfrich, H. P., Optimale lineare Approximation beschränkter Mengen in normierten Räumen. Erscheint demnächst. · Zbl 0225.41005
[15] Hubbard, B. E., Remarks on the Order of Convergence in the Discrete Dirichlet Problem. In: Numerical Solution of Partial Differential Equations. New York: Academic Press 1966, S. 21–34.
[16] Katsanis, Th., A numerical method for the solution of certain Neumann problems. SIAM J. Appl. Math. 16, 723–731 (1968). · Zbl 0165.18302 · doi:10.1137/0116059
[17] Kellogg, R. B., Difference equations on a mesh arising from a general triangulation. Math. Comp. 18, 203–210 (1964). · Zbl 0119.12403 · doi:10.1090/S0025-5718-1964-0177517-7
[18] Kellogg, R. B., An error estimate for elliptic difference equations on a convex polygon. SIAM J. Numer. Anal. 3, 79–90 (1966). · Zbl 0143.17602 · doi:10.1137/0703006
[19] Laasonen, P., On the solution of Poisson’s difference equation. J. the Association for Computing Machinery 5, 370–382 (1958). · Zbl 0087.12202 · doi:10.1145/320941.320951
[20] Lorentz, G. G., Approximation of Functions. New York: Holt, Rinehart and Winston 1966. · Zbl 0153.38901
[21] Mihlin, C. G., Some properties of polynomial approximations according to Ritz. Dokl. Akad. Nauk SSSR 180, 276–278 (1968); Soviet Math. 9, 614–616 (1968).
[22] Necas, J., Les méthodes discrètes en théorie des équations élliptiques. Paris: Masson & Cie. Academia Prague 1967.
[23] Nitsche, J., Zur Frage optimaler Fehlerschränken bei Differenzenverfahren. Rend. Circ. Mat. Palermo 16, 69–80 und 233–238 (1967). · Zbl 0189.49002 · doi:10.1007/BF02844086
[24] Nitsche, J., Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens. Numer. Math. 11, 346–348 (1968). · Zbl 0175.45801 · doi:10.1007/BF02166687
[25] Nitsche, J. A., & J. C. C. Nitsche, Error estimates for the numerical solution of elliptic differential equations. Arch. Rational Mech. Anal. 5, 293–306 (1960). · Zbl 0097.33103 · doi:10.1007/BF00252911
[26] Oganesjan, L. A., Convergence of difference schemes in case of improved approximation of the boundary. Z. Vycisl. Mat. i Mat. Fiz. 6, 1029–1042 (1966).
[27] Sobolev, S. L., Applications of Functional Analysis in Mathematical Physics. Am. Math. Soc., Providence, 1963. · Zbl 0123.09003
[28] Thomée, V., On the convergence of difference quotients in elliptic problems. Technical Note BN-537, Chalmers Institute of Technology, Göteborg, April 1968.
[29] Veidinger, L., Über die Abschätzung des Fehlers bei finiten Differenzen. Stud. Sci. Mat. Hungarica 2, 185–191 (1967). · Zbl 0155.20203
[30] Zlamal, M., On the finite element method. Numer. Math. 12, 394–409 (1968). · Zbl 0176.16001 · doi:10.1007/BF02161362
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.