Numerical methods for reaction-diffusion problems with non-differentiable kinetics
type: Item
instance of: scholarly article
title: Numerical methods for reaction-diffusion problems with non-differentiable kinetics
zbMATH Open document ID: 0655.65127
DOI: 10.1007/BF01395875
author: A. B. Stephens
author: Manil Suri
author: A. Kadir Aziz
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133262
review text: A class of steady-state semilinear reaction-diffusion problems with non- differential kinetics is considered. It is described by the scalar equation \(\Delta u=\lambda f(u(x)),\) \(0<\lambda =const\), \(x\in \Omega\) (u\(\geq 0\) in \(\Omega)\), \(u=1\), \(x\in \partial \Omega\), with \(\Omega\) \(\subset R\) n, \(n=1,2,3\), \(f(t)=t\) p if \(t>0\), \(0<p<1\), \(f(t)=0\), if \(t\leq 0.\) For a finite element scheme with linear triangular elements the estimates \(\| v-v\) \(h\| \leq ch\), if \(0.5<p<1\), and \(\| v-v\) \(h\| \leq ch^{2p}\), if \(0<p<0.5\), are proved in which v is the exact solution of the problem, v h is the finite element solution and \(\| \cdot \|\) is the norm in the Sobolev space H 1(\(\Omega)\). The authors note that their numerical results show that for all \(p\in (0,1)\) the rate of convergence is O(h).
reviewed by: Vladimir D. Korneev
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 4070246
zbMATH Keywords: steady-state semilinear reaction-diffusion problems
zbMATH Keywords: finite element scheme
zbMATH Keywords: estimates
zbMATH Keywords: rate of convergence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4070246