Pointwise Bounds for Discrete Green’s Functions

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Previous article Next article Pointwise Bounds for Discrete Green’s FunctionsJ. H. Bramble and V. ThoméeJ. H. Bramble and V. Thoméehttps://doi.org/10.1137/0706053PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. H. Bramble, On the convergence of difference approximations to weak solutions of Dirichlet's problem, Numer. Math., 13 (1969), 101–111 10.1007/BF02163229 MR0250495 0196.17803 CrossrefISIGoogle Scholar[2] James H. Bramble, On the convergence of difference approximations for second order uniformly elliptic operatorsNumerical Solution of Field Problems in Continuum Physics (Proc. Sympos. Appl. Math., Durham, N.C., 1968), SIAM-AMS Proc., Vol. II, Amer. Math. Soc., Providence, R. I., 1970, 201–209 MR0260200 0234.65086 Google Scholar[3] J. H. Bramble, , B. E. Hubbard and , Vidar Thomée, Convergence estimates for essentially positive type discrete Dirichlet problems, Math. Comp., 23 (1969), 695–709 MR0266444 0217.21902 CrossrefISIGoogle Scholar[4] J. H. Bramble, , B. E. Hubbard and , M. Zlámal, Discrete analogues of the Dirichlet problem with isolated singularities, SIAM J. Numer. Anal., 5 (1968), 1–25 10.1137/0705001 MR0239770 0176.46902 LinkISIGoogle Scholar[5] James R. Kuttler, Finite difference approximations for eigenvalues of uniformly elliptic operators, SIAM J. Numer. Anal., 7 (1970), 206–232 10.1137/0707014 MR0273841 0208.42601 LinkISIGoogle Scholar[6] Pentti Laasonen, On the solution of Poisson's difference equation, J. Assoc. Comput. Mach., 5 (1958), 370–382 MR0121999 0087.12202 CrossrefISIGoogle Scholar[7] Vidar Thomée and , Bertil Westergren, Elliptic difference equations and interior regularity, Numer. Math., 11 (1968), 196–210 MR0224303 0159.38204 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Asymptotics of the heat kernels on 2D latticesAsymptotic Analysis, Vol. 112, No. 1-2 | 6 Mar 2019 Cross Ref On Solving the Singular System Arisen from Poisson Equation with Neumann Boundary ConditionJournal of Scientific Computing, Vol. 69, No. 1 | 4 April 2016 Cross Ref Petrov–Galerkin finite element approximation for the three dimensional well modelJournal of Computational and Applied Mathematics, Vol. 277 | 1 Mar 2015 Cross Ref A 3-dimensional well model in the flow transport through porous mediaApplied Mathematical Modelling, Vol. 38, No. 21-22 | 1 Nov 2014 Cross Ref On the decay of the inverse of matrices that are sum of Kronecker productsLinear Algebra and its Applications, Vol. 452 | 1 Jul 2014 Cross Ref On Sojourn Times in the M/ M/1-PS Model, Conditioned on the Number of Other UsersApplied Mathematics Research eXpress, Vol. 11 | 19 February 2010 Cross Ref A kernel-free boundary integral method for elliptic boundary value problemsJournal of Computational Physics, Vol. 227, No. 2 | 1 Dec 2007 Cross Ref On the accuracy of finite difference methods for elliptic problems with interfacesCommunications in Applied Mathematics and Computational Science, Vol. 1, No. 1 | 31 December 2006 Cross Ref Least squares methods for elliptic systemsMathematics of Computation, Vol. 44, No. 169 | 1 January 1985 Cross Ref L�sung des Dirichletproblems und Konvergenz der Differenzenapproximation f�r elliptische Differentialgleichungen zweiter OrdnungMathematische Zeitschrift, Vol. 131, No. 3 | 1 Sep 1973 Cross Ref Discrete Green’s functionsMathematics of Computation, Vol. 27, No. 121 | 1 January 1973 Cross Ref The distribution of the eigenvalues of the discrete LaplacianBIT, Vol. 12, No. 4 | 1 Dec 1972 Cross Ref A fourth-order finite-difference approximation for the fixed membrane eigenproblemMathematics of Computation, Vol. 25, No. 114 | 1 January 1971 Cross Ref Volume 6, Issue 4| 1969SIAM Journal on Numerical Analysis523-616 History Submitted:14 November 1968Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706053Article page range:pp. 583-590ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics