Finite element approximation of a sixth order nonlinear degenerate parabolic equation
type: Item
instance of: scholarly article
title: Finite element approximation of a sixth order nonlinear degenerate parabolic equation
zbMATH Open document ID: 1041.65076
author: John W. Barrett
author: S. Langdon
author: Robert Nürnberg
published in: Numerische Mathematik
publication date: 2004-03-11T00:00:00Z
full work available at URL: sixth2d.pdf
review text: Degenerate nonlinear parabolic problems of the type \(u_t=\nabla(b(u)\nabla\Delta^2u)\) with \(b(u)=| u| ^\gamma\) where \(\gamma\in(0,+\infty)\) are considered. Its finite element treatment is based upon the equivalent mixed formulation \[ u_t=\nabla(b(u)\nabla w),\quad w=-\Delta v,\quad v=-\Delta u\,. \] Spatial discretizations by continuous linear finite elements over simplices that partition the polyhedral domain are studied. For the time integration an semi-implicit Euler scheme with frozen coefficients is applied. Moreover, a physically required nonnegativity is included via variational inequalities. In detail, analytical properties are investigated and convergence of the proposed method including an iterative scheme for the discrete problem is shown.
reviewed by: Christian Grossmann
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 2055238
zbMATH Keywords: degenerate parabolic equations
zbMATH Keywords: finite elements
zbMATH Keywords: semi-implicit Euler method
zbMATH Keywords: convergence
MaRDI profile type: Publication
OpenAlex ID: W1998903284
Wikidata QID: Q117202815
DOI: 10.1007/S00211-003-0479-4
description: scientific article; zbMATH DE number 2055238