scholarly journals Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem

2005 ◽  
Vol 14 (1) ◽  
pp. 221-234 ◽  
Author(s):  
Juan-Luis Vázquez ◽  
Philippe Souplet
Keyword(s):  
Steady State ◽  
Blow Up ◽  
Convection Problem ◽  
Diffusion Convection ◽  
Singular Steady State

scholarly journals Convergence to a singular steady state of a parabolic equation with gradient blow-up

2007 ◽  
Vol 20 (5) ◽  
pp. 578-582 ◽  
Author(s):  
Marek Fila ◽  
Jari Taskinen ◽  
Michael Winkler
Keyword(s):  
Steady State ◽  
Parabolic Equation ◽  
Blow Up ◽  
Singular Steady State

Convection Problems on Anisotropic Meshes

2013 ◽  
Vol 13 (1) ◽  
pp. 55-78
Author(s):  
Carola Kruse ◽  
Matthias Maischak
Keyword(s):  
Steady State ◽  
Transport Problem ◽  
Annular Domain ◽  
Discontinuous Solutions ◽  
Continuous Solutions ◽  
Edge Singularity ◽  
Unit Square ◽  
Anisotropic Meshes ◽  
Theoretical Part ◽  
Convection Problem

Abstract. The Galerkin and SDFEM methods are compared for a steady state convection problem. The theoretical part of this work deals with the development of approximation results for continuous solutions on the unit square containing an edge singularity. In the numerical part we verify those approximation results by considering continuous as well as discontinuous solutions to the transport problem on an annular domain with a singularity at the inner circle.

Identification of a Steady-State Flow in Porous Media Using Artificial Neural Networks

2012 ◽  
Author(s):  
Marek J. Lefik ◽  
Daniela P. Boso ◽  
Bernhard A. Schrefler
Keyword(s):  
Neural Networks ◽  
Porous Media ◽  
Artificial Neural Networks ◽  
Steady State ◽  
Concentration Field ◽  
Flow In Porous Media ◽  
Homogeneous Field ◽  
Steady State Flow ◽  
Convection Problem ◽  
Artificial Neural

For a steady state convection problem, assuming given concentration field values in a few measurement points and hydraulic head values in the same piezometers, the source of the concentration, and its intensity are deduced using Artificial Neural Networks (ANNs). ANNs are trained with data extracted from Finite Difference (FD) solution of a classical convection problem for small Peclet number. The numerical analysis is exemplified for vanishing, homogeneous and non-homogeneous field of velocity. It is shown that the diffusivity vector can also be identified. The complexity of the problem is discussed for each studied case.

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