2 edition of **Maximum principle in finite elements models for cconvection-diffusion phenomena** found in the catalog.

Maximum principle in finite elements models for cconvection-diffusion phenomena

Tsutomu Ikeda

- 230 Want to read
- 17 Currently reading

Published
**1983**
by North-Holland Pub. Co. in Amsterdam
.

Written in English

- Diffusion,
- Finite element method.

**Edition Notes**

Bibliography: p. 137-141.

Statement | Tsutomu Ikeda. |

Series | North-Holland mathematics studies -- 76, Lecture notes in numerical and applied analysis -- v. 4 |

Classifications | |
---|---|

LC Classifications | QC185 I43 1983 |

The Physical Object | |

Pagination | ix 159 p. : |

Number of Pages | 159 |

ID Numbers | |

Open Library | OL19786784M |

ISBN 10 | 0444865963 |

phenomena. We consider mathematical models that express certain conservation principles and consist of convection-diffusion-reactionequations written in integral, differential, or weak form. In particular, we discuss the qualitative properties of exact solutions to model problems of elliptic, hyperbolic, and parabolic type. Next. Enforcing the Discrete Maximum Principle for Linear Finite Element Solutions of Second-Order Elliptic Problems Richard Liska1,∗ and Mikhail Shashkov2 1 Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Brˇehova´ 7, 19 Prague 1, Czech Republic.

An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes. A maximum-principle preserving C 0 finite element method for scalar conservation equations, A monotone finite element scheme for convection–diffusion equations, by: Browse other questions tagged pde maximum-principle parabolic-pde or ask your own question. The Overflow Blog How the pandemic changed traffic trends from M visitors across Stack.

Finite Element Method Introduction, 1D heat conduction 10 Basic steps of the finite-element method (FEM) 1. Establish strong formulation Partial differential equation 2. Establish weak formulation Multiply with arbitrary field and integrate over element 3. Discretize over space Mesh generation 4. Select shape and weight functions Galerkin method 5. Using the Laplace–Beltrami problem on an implicitly defined surface $\Gamma$ as a model PDE, we define Lagrange finite element methods of arbitrary degree on polynomial approximations to $\Gamma$ which likewise are of arbitrary degree. Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary Cited by:

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Maximum Principle in Finite Element Models for Convection-diffusion Phenomena (Mathematics Studies) [Tsutomu Ikeda] on *FREE* shipping on qualifying offers. Maximum Principle in Finite Element Models for Convection-diffusion Phenomena (Mathematics Studies): Tsutomu Ikeda: : BooksCited by: Search in this book series.

Maximum Principle in Finite Element Models for Convection-Diffusion Phenomena. Edited by Tsutomu Ikeda. Vol Pages iii-vii, () Download full volume. Previous volume. Next volume. Actions for selected chapters. Select all / Deselect all.

Maximum principle in finite element models for convection-diffusion phenomena. Amsterdam ; New York: North-Holland Pub. Co., (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Tsutomu Ikeda.

Maximum principle in finite element models for convection-diffusion phenomena. Amsterdam ; New York: North-Holland Pub. Co., (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Tsutomu Ikeda.

Ikeda, T.: Maximum principle in finite element models for convection-diffusion phenomena. LN in Numerical and Applied Analysis, 4, North-Holland Mathematics Studies, Kinokuniya Book Store Co. Ltd. Tokyo, Google ScholarCited by: [23] Ikeda T., Maximum Principle in Finite Element Models for Convection-Diffusion Phenomena, Lecture Notes Numer.

Appl. Anal., 4, Kinokuniya Book Store, Tokyo, [24] Karátson J., Korotov S., Discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions, Numer.

Ikeda, Maximum Principle in Finite Element Models for Convection–Diffusion Phenomena, North-Holland, Amster- dam, [12] S. Korotov, M. Kˇrížek, P. Neittaanmäki, Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle, Math.

Cited by: Maximum Principle in Finite Element Models for Convection-Diffusion Phenomena, () Piecewise continuous discretization techniques for initial value problems with applications to Cited by: T. Ikeda, Maximum Principle in Finite Element Models for Convection–Diffusion Phenomena, Lecture Notes in Numerical and Applied Analysis, vol.

4, North Cited by: on the right-hand side of the same equation. This means that the maximum of our solution can only be found on the boundary. What we just proved is called the strong maximum principle. There is also the weak maximum principle, which holds when the source term is allowed to be zero; i.e., f\le0 is the condition.

In this case, the maximum is either at the boundary or the solution. () A discrete maximum principle for the weak Galerkin finite element method on nonuniform rectangular partitions. Numerical Methods for Partial Differential Equations() The finite volume scheme preserving maximum principle for diffusion equations with discontinuous by: 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 Cited by: 7. Discrete maximum principle for finite element parabolic models in higher dimensions which typically arise from some basic principles of the modelled phenomena.

In this paper we investigate this question for the numerical solution of initial-boundary problems for the parabolic problems in higher dimensions, with the first boundary condition Cited by: 4. InH. Fujii investigated discrete versions of the maximum principle for the model heat equation using piecewise linear finite elements in space.

Early discussion of the discrete maximum principle for the convection diffusion equations includes the linear finite element solutions for parabolic equations [12] with recent developments in [ SIAM Journal on Numerical AnalysisReferences. Maximum Principle in Finite Element Models for Convection-Diffusion Phenomena, (Italy) in the context of the Program of Preventive Medicine.

Nonlinear Phenomena in Mathematical Sciences, Topics in finite element discretization of parabolic evolution Cited by: The discrete maximum principle for linear simplicial finite element approximations of a reaction–diffusion problem. Linear Algebra Appl.– Cited by: [23] Ikeda T., Maximum Principle in Finite Element Models for Convection-Diffusion Phenomena, Lecture Notes Numer.

Appl. Anal., 4, Kinokuniya Book Store, Tokyo, Google Scholar [24] Karátson J., Korotov S., Discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions, by: 7. Continuous Maximum Principle • The classical (smooth) solutions of many elliptic/parabolic problems are known to satisfy various (continuous) maximum principles (or CMPs in short).

For our model elliptic problem standard CMP reads as follows: f ≤ 0 =⇒ max x∈Ω u(x) ≤ max{0, max s∈∂Ω g(s)}. (3). Discrete maximum principle for the finite element solution of linear non-stationary diffusion–reaction problems numerical modelling of various real-life phenomena (heat conduction, air.

A MONOTONE FINITE ELEMENT SCHEME FOR CONVECTION-DIFFUSION EQUATIONS JINCHAO XU AND LUDMIL ZIKATANOV Abstract. A simple technique is given in this paper for the construction and analysisof aclassof niteelement discretizations forconvection-di usion prob-lems in any spatial dimension by properly averaging the PDE coe cients on element edges.() Discrete maximum principle for the finite element solution of linear non-stationary diffusion–reaction problems.

Applied Mathematical Modelling() Sufficient conditions of the discrete maximum–minimum principle for parabolic problems on rectangular by: Remark For a discussion on necessary constraints on a finite element mesh to satisfy maximum principles and the non-negative constraint, see references [18,16, 31, 52,50].

However, all these Author: Róbert Horváth.