Finite difference approximation of a parabolic problem with variable coefficients
type: Item
instance of: scholarly article
title: Finite difference approximation of a parabolic problem with variable coefficients
zbMATH Open document ID: 1349.65389
DOI: 10.2298/PIM1409049J
author: Boško S. Jovanović
author: Zorica D. Milovanović
publication date: 2016-06-27T00:00:00Z
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 6598860
zbMATH Keywords: parabolic initial-boundary-value problem
zbMATH Keywords: oblique derivative boundary condition
zbMATH Keywords: finite differences
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: convergence
zbMATH Keywords: variable coefficients
zbMATH Keywords: error bounds
MaRDI profile type: Publication
published in: Publications de l'Institut Mathématique. Nouvelle Série
review text: The convergence of a finite difference scheme that approximates the third initial-boundary-value problem for parabolic equation with variable coefficients on a unit square is considered. We assume that the generalized solution of the problem belongs to the Sobolev space \(W_2^{s,s/2}\), \(\,s\leq 3\). An almost second-order convergence rate estimate (with additional logarithmic factor) in the discrete \(W^{1,1/2}_2\) norm is obtained. The obtained error bounds are compatible with the smoothness of the data. The result is based on some nonstandard a priori estimates involving fractional order discrete Sobolev norms.
description: scientific article; zbMATH DE number 6598860