Discrete maximum principle for finite-difference operators

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

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).

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.

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.

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).

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

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).

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).

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).

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

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

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

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.

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

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

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

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

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

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

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