A numerical procedure for the porous media equation
type: Item
instance of: scholarly article
title: A numerical procedure for the porous media equation
zbMATH Open document ID: 0608.76083
DOI: 10.1016/0898-1221(85)90156-7
author: Eduardo Socolovsky
author: Richard C. MacCamy
publication date: 1985-01-01T00:00:00Z
review text: The paper is concerned with an attempt to derive a procedure for obtaining the numerical solution of the porous medium problem \(u_ t=(u^ 2)_{xx}\), \(u(0,x)=u_ 0(x)\), \(u_ 0(x)\geq 0\), \(t>0\), \(x\in R\). The problem appears to be parabolic but it has some distinctly hyperbolic features. The boundary is also a moving one. The approach uses a variational formulation. The idea of finite elements is used. Numerical results are presented for a particular situation. Stability is obtained. The paper will be interesting to numerical analysis.
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 65Z05
zbMATH DE Number: 3984856
zbMATH Keywords: moving boundary
zbMATH Keywords: numerical solution
zbMATH Keywords: porous medium problem
zbMATH Keywords: variational formulation
zbMATH Keywords: finite elements
zbMATH Keywords: Stability
MaRDI profile type: Publication
full work available at URL: 0898-1221(85)90156-7
OpenAlex ID: W1982615630
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cites work: DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 3984856