Displaying similar documents to “Weak discrete maximum principles”

Discrete maximum principle for interior penalty discontinuous Galerkin methods

Tamás Horváth, Miklós Mincsovics (2013)

Open Mathematics

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A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness...

About Delaunay triangulations and discrete maximum principles for the linear conforming FEM applied to the Poisson equation

Reiner Vanselow (2001)

Applications of Mathematics

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The starting point of the analysis in this paper is the following situation: “In a bounded domain in ℝ 2 , let a finite set of points be given. A triangulation of that domain has to be found, whose vertices are the given points and which is ‘suitable’ for the linear conforming Finite Element Method (FEM).” The result of this paper is that for the discrete Poisson equation and under some weak additional assumptions, only the use of Delaunay triangulations preserves the maximum principle. ...

Multipoint boundary value problems for discrete equations

Pavel Drábek, Harold Bevan Thompson, Christopher Tisdell (2001)

Commentationes Mathematicae Universitatis Carolinae

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In this work we establish existence results for solutions to multipoint boundary value problems for second order difference equations with fully nonlinear boundary conditions involving two, three and four points. Our results are also applied to systems.

A discrete maximum principle

Tadeusz Styś

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CONTENTSIntroduction......................................................................................................................................... 5§ 1. A maximum principle for linear mappings.................................................................................... 6§ 2. A maximum principle for nonlinear mappings............................................................................. 9§ 3. A finite difference analogue of a maximum principle for nonlinear elliptic...

The discrete maximum principle for Galerkin solutions of elliptic problems

Tomáš Vejchodský (2012)

Open Mathematics

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This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The...