Variable time-step \(\vartheta\)-scheme for nonlinear evolution equations governed by a monotone operator
type: Item
instance of: scholarly article
title: Variable time-step \(\vartheta\)-scheme for nonlinear evolution equations governed by a monotone operator
zbMATH Open document ID: 1177.65075
author: Etienne Emmrich
published in: Calcolo
publication date: 2009-10-19T00:00:00Z
review text: This paper is concerned with time-discretisation of the initial-value problems for nonlinear evolution equation of the form \(u'+Au=f\) in \((0, T)\), \(u(0)=u_0\) and its generalizations. Here \(A\) is a Nemytskii operator corresponding to a family of hemicontinuous operators. In this paper it is proved the convergence of piecewise polynomial prolongations of the discrete numerical solutions towards the weak solution without requiring any additional regularity of the exact solution. The method of proof relies on the theory of monotone operators and ompactness arguments combined with algebraic relations that describe properties of the temporal discretization.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 65J08
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 47J35
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35K90
zbMATH DE Number: 5618000
zbMATH Keywords: monotone operator
zbMATH Keywords: time discretization
zbMATH Keywords: non-uniform grid
zbMATH Keywords: convergence
zbMATH Keywords: nonlinear evolution equation
MaRDI profile type: Publication
full work available at URL: s10092-009-0007-8
OpenAlex ID: W2092194508
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DOI: 10.1007/S10092-009-0007-8
description: scientific article; zbMATH DE number 5618000