Energy methods for numerical analysis
type: Item
instance of: scholarly article
title: Energy methods for numerical analysis
zbMATH Open document ID: 1088.65101
author: Reiko Sakamoto
published in: Tsukuba Journal of Mathematics
publication date: 2006-03-28T00:00:00Z
review text: In a quite inaccurate formulation of a class of linear boundary value problems the author introduces an elliptic type inequality for the adjoint operator of the original problem which is termed the ``energy inequality''. Accordingly he proves the existence, uniqueness and regularity results for solutions. Then he adds a nonlinear term and tries to prove the same result using some successive approximation schemes. However, it seems that he is not aware of the classical theory concerning elliptic boundary value problems.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 5015598
zbMATH Keywords: linear boundary value problems
zbMATH Keywords: energy inequality
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: nonlinear boundary value problems
zbMATH Keywords: successive approximations
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496164896
OpenAlex ID: W616806978
DOI: 10.21099/TKBJM/1496164896
description: scientific article; zbMATH DE number 5015598