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Discrete maximum principle for finite-difference operators

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References

  1. Bramble, J. H.,Error Estimates for Difference Methods in Forced Vibration Problems, SIAM J. Numer. Anal.3, 1–12 (1966).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  3. Bramble, J. H., andHubbard, B. E.,A Priori Bounds on the Discretization Error in the Numerical Solution of the Dirichlet Problem, Contributions to Differential Equations, Vol. II (John Wiley & Sons, Inc., New York, 1963), pp. 229–252.

    Google Scholar 

  4. Bramble, J. H. andHubbard, B. E.,A Theorem on Error Estimation for Finite Difference Analogues of the Dirichlet Problem for Elliptic Equations, Contributions to Differential Equations, Vol. II (John Wiley & Sons, Inc., New York 1963), pp. 319–340.

    Google Scholar 

  5. Bramble, J. H. andHubbard, B. E.,On a Finite Difference Analogue of an Elliptic Boundary Problem which is Neither Diagonally Dominant Nor of Non-Negative Type, J. Math. and Phys.43, 117–132 (1964).

    Google Scholar 

  6. Bramble, J. H. andHubbard, B. E.,New Monotone Type Approximations for Elliptic Problems, Math. Comp.18, 349–367 (1964).

    Google Scholar 

  7. 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).

    Article  Google Scholar 

  8. Bramble, J. H. andHubbard, B. E.,Approximations of Solutions of Mixed Boundary Value Problems for Poisson's Equation by Finite Differences, J. Assoc. Comput. Mach.12, 114–123 (1965).

    Google Scholar 

  9. Bramble, J. H., Hubbard, B. E. andZlamal, M.,Discrete Analogues of the Dirichlet Problem with Isolated Singularities, SIAM J. Numer. Anal.5, 1–25 (1968).

    Article  Google Scholar 

  10. Collatz, L.,The Numerical Treatment of Differential Equations, 3rd. ed. (Springer-Verlag, New York 1966).

    Google Scholar 

  11. Courant, R., andHilbert, D.,Methods of Mathematical Physics, Vol. II (Interscience Publishers, New York 1962)

    Google Scholar 

  12. Forsythe, G. E. andWasow, W. R.,Finite-Difference Methods for Partial Differential Equations (John Wiley & Sons, Inc., New York 1960).

    Google Scholar 

  13. Hubbard, B. E.,Remarks on the Order of Convergence in the Discrete Dirichlet Problem, Numerical Solution of Partial Differential Equations (Academic Press, New York 1966), pp. 21–34.

    Google Scholar 

  14. Kellog, R. B.,Difference Equations on a Mesh Arising from a General Triangulation, Math. Comp.18, 203–210 (1964).

    Google Scholar 

  15. Kellog, R. B.,An Error Estimate for Elliptic Difference Equations on a Convex Polygon, SIAM J. Numer. Anal.3, 79–90 (1966).

    Article  Google Scholar 

  16. Mcallister, G. T.,Quasilinear Uniformly Elliptic Partial Differential Equations and Difference Equations, SIAM J. Numer. Anal.3, 13–33 (1966).

    Article  Google Scholar 

  17. Mac Neal, R. H.,An Asymmetrical Finite Difference Network, Quart. Appl. Math.11, 295–310 (1953).

    Google Scholar 

  18. Price, H. S.,Monotone and Oscillation Matrices Applied to Finite Difference Approximations, Math. Comp.22, 489–516 (1968).

    Google Scholar 

  19. Varga, R. S.,Matrix Iterative Analysis (Prentice-Hall, Inc., Englewood Cliffs, N.J. 1962).

    Google Scholar 

  20. Varga, R. S.,On a Discrete Maximum Principle, SIAM J. Numer. Anal.3, 355–359 (1966).

    Article  Google Scholar 

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Ciarlet, P.G. Discrete maximum principle for finite-difference operators. Aeq. Math. 4, 338–352 (1970). https://doi.org/10.1007/BF01844166

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