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Survey of discrete maximum principles for linear elliptic and parabolic problems
We survey techniques for proving discrete maximum principles for finite element approximations of linear elliptic and parabolic problems. Special emphasis is laid on approximations built on tetrahedral meshes....
BA - Obecná matematika
- 2004 •
- D
Rok uplatnění
D - Stať ve sborníku
The discrete maximum principle for Galerkin solutions of elliptic problems
of the discrete maximum principle for the higher-order finite elements in one-dimension the state of the art in the field of the discrete maximum principle and provides newThis paper provides an ...
BA - Obecná matematika
- 2012 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Discrete Maximum Principle for a 1D Problem with Piecewise-Constant Coefficients Solved by hp-FEM
In this paper we prove the discrete maximum principle for a one-dimensional equation of the form - (au´)´= f with piecewise-constant coefficient a(x), discretized by the hp-FEM. The discrete problem is tra...
BA - Obecná matematika
- 2007 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Discrete Green´s Function and Maximum Principles
In this paper the discrete Green´s function (DGF) is introduced and its fundamental properties are proven. Further it is indicated how to use these results to prove the discrete maximum principle for 1D Poisson equ...
BA - Obecná matematika
- 2006 •
- D
Rok uplatnění
D - Stať ve sborníku
On a Discrete Maximum Principle for Linear FE Solutions of Elliptic Problems with a Nondiagonal Coefficient Matrix
In this paper we present a sufficient condition for the validity of a discrete maximum principle for a class of elliptic problems of the second order with a nondiagonal coefficient matrix, solved by means of linear finite e...
BA - Obecná matematika
- 2009 •
- D
Rok uplatnění
D - Stať ve sborníku
On weakening conditions for discrete maximum principles for linear finite element schemes
In this work we discuss weakening requirements on the set of sufficient conditions due to Ph. Ciarlet for matrices associated to linear finite element schemes, which is commonly used for proving validity of discrete maximum prin...
BA - Obecná matematika
- 2009 •
- D
Rok uplatnění
D - Stať ve sborníku
Numerical solution of convection-diffusion equations using upwinding techniques satisfying the discrete maximum principle
We discuss the application of the finite element method to the numerical solution of scalar two-dimensional steady convection-diffusion equations with the emphasis on upwinding techniques satisfying the discrete maximum principl...
BA - Obecná matematika
- 2006 •
- D
Rok uplatnění
D - Stať ve sborníku
Discrete maximum principle for parabolic problems solved by prismatic finite elements
In this paper we analyze the discrete maximum principle (DMP) for a non-stationary diffusion reaction problem solved by means of prismatic finite elements and theta-method. We derive geometric conditions on the shape parame...
BA - Obecná matematika
- 2010 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
The discrete maximum principle for linear simplicial finite element approximations of a reaction-diffusion problem
This paper provides a sufficient condition for the discrete maximum principle for a fully discrete linear simplicial finite element discretization of a reaction-diffusion problem to hold....
BA - Obecná matematika
- 2008 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Discrete maximum principle for Poisson equation with mixed boundary conditions solved by hp-FEM
We present a proof of the discrete maximum principle (DMP) for the 1D Poisson equation equipped with mixed Dirichlet-Neumann boundary conditions. The problem is discretized using finite elements of arbitrary length...
BA - Obecná matematika
- 2009 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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