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Ciarlet, Philippe G.

Discrete variational Green’s function. I. (English) Zbl 0194.12703

Aequationes Math. 4, 74-82 (1970).
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Cited in 9 Documents

MSC:

35J08 Green’s functions for elliptic equations

Keywords:

Green’s function; linear elliptic operator; variational approximation procedure
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\textit{P. G. Ciarlet}, Aequationes Math. 4, 74--82 (1970; Zbl 0194.12703)
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References:

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[2] Bramble, J. H., andHubbard, B. E.,On the Formulation of Finite Difference Analogues of the Dirichlet Problem for Poisson’s Equation, Numer. Math.4, 313–327 (1962). · Zbl 0135.18102
[3] Bramble, J. H., andHubbard, B. E.,On a Finite Difference Analog of an Elliptic Boundary Problem which is Neither Diagonally Dominant nor of Non-Negative Type, J. Math. Phys.43, 117–132 (1964). · Zbl 0126.32305
[4] Bramble, J. H., andHubbard, B. E.,Approximation of Solutions of Mixed Boundary Value Problems for Poisson’s Equation by Finite Differences, J. Assoc. Comput. Mach.12, 114–123 (1965). · Zbl 0125.07305
[5] Bramble, J. H., andHubbard, B. E.,A Finite Difference Analog of the Neumann Problem for Poisson’s Equation, SIAM J. Numer. Anal.2, 1–14 (1965). · Zbl 0141.33201
[6] Ciarlet, P. G., Schultz, M. H. andVarga, R. S.,Numerical Methods of High-Order Accuracy for Nonlinear Boundary Value Problems, I:One Dimensional Problem, Numer. Math.9, 394–430 (1967). · Zbl 0155.20403
[7] Ciarlet, P. G., Schultz, M. H. andVarga, R. S.,Numerical Methods of High-Order Accuracy for Nonlinear Boundary Value Problems, III:Eigenvalue Problems, to appear in Numer. Math. (1968).
[8] Courant, R., andHilbert, D.,Methods of Mathematical Physics Vol. 1 (Interscience, New-York 1953). · Zbl 0051.28802
[9] Courant, R., andHilbert, D.,Methods of Mathematical Physics, Vol. 2 (Interscience, New-York 1962). · Zbl 0099.29504
[10] Hubbard, B.,Remarks on the Order of Convergence in the Discrete Dirichlet Problem, inNumerical Solution of Partial Differential Equations,J. H. Bramble, ed. (Academic Press, New-York 1966), pp. 21–34.
[11] Lions, J. L.,Equations différentielles opérationnelles (Springer-Verlag, Berlin 1961).
[12] Malgrange, B.,Existence et approximation des solutions des équations aux dérivées partielles, Ann. Inst. Fourier (Grenoble)6, 3–86 (1955).
[13] Mikhlin, S. G.,Variational Methods in Mathematical Physics (Pergamon Press, Oxford 1964). · Zbl 0119.19002
[14] Nečas, J.,Les méthodes directes en théorie des équations elliptiques (Masson, Paris 1967).
[15] Yosida, K. Y.,Functional Analysis (Springer-Verlag, Berlin 1966). · Zbl 0152.32102
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.