A numerical procedure for diffusion subject to the specification of mass
type: Item
instance of: scholarly article
title: A numerical procedure for diffusion subject to the specification of mass
zbMATH Open document ID: 0773.65069
DOI: 10.1016/0020-7225(93)90010-R
author: John R. Cannon
author: Alec L. Matheson
published in: International Journal of Engineering Science
publication date: 1993-06-29T00:00:00Z
review text: The authors look for the numerical solution of the diffusion problem \(u_ t-u_{xx}=s\), \(0<x<1\), \(0<t\leq T\), subject to the initial condition \(u(x,0)=f(x)\), \(0<x<1\), to the boundary condition \(u(1,t)=g(t)\), \(0<t\leq T\), and to the mass specification condition \(\int^{b(t)}_ 0u(x,t)dx=m(t)\), \(0<b(t)<1\), for given functions \(s,f,g,b\) and \(m\). Using maximum principle arguments, the authors establish a pointwise a priori estimate for \(| u_ x(x,t)|\) yielding a similar estimate for \(\max| u(x,t)|\). Similar arguments lead to the stability estimate for the finite difference scheme providing an \(O(h^ 2+\tau)\) approximation to an equivalent problem. The influence of the input data error together with the truncation error on the finite difference solution is studied theoretically as well as numerically.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 220563
zbMATH Keywords: stability
zbMATH Keywords: error estimate
zbMATH Keywords: diffusion problem
zbMATH Keywords: mass specification
zbMATH Keywords: maximum principle
zbMATH Keywords: finite difference scheme
reviewed by: Ulrich Langer
MaRDI profile type: Publication
cites work: Q3682852
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description: scientific article; zbMATH DE number 220563