Study of the convergence of the finite-element method for parabolic equations with a nonlinear nonlocal spatial operator
type: Item
instance of: scholarly article
title: Study of the convergence of the finite-element method for parabolic equations with a nonlinear nonlocal spatial operator
zbMATH Open document ID: 1338.65224
DOI: 10.1134/S001226611507006X
author: D. Kharzeev
published in: Differential Equations
publication date: 2015-10-14T00:00:00Z
review text: This paper is interested in a parabolic equation with a nonlinear non-local spatial operator. The considered spatial operator depends nonlinearly on the unknown function, its gradient, but also on a non-local (integral) spatial characteristic of the solution. The problem is semi-discretized with respect to the time \(t\). Then the finite element method is used for space discretization. The approximate solution is sought with the non-local characteristic resolved from the previous time level. The convergence of the constructed algorithm under minimal assumptions on the smoothness of the original data is proven.
reviewed by: Petr Sváček
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 6493786
zbMATH Keywords: finite element method
zbMATH Keywords: stability
zbMATH Keywords: semidiscretization
zbMATH Keywords: nonlinear parabolic equation
zbMATH Keywords: convergence
zbMATH Keywords: algorithm
MaRDI profile type: Publication
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full work available at URL: s001226611507006x
OpenAlex ID: W1121120541
description: scientific article; zbMATH DE number 6493786