The boundary-domain integral method for elliptic systems. With an application to shells
type: Item
instance of: scholarly article
title: The boundary-domain integral method for elliptic systems. With an application to shells
zbMATH Open document ID: 0894.65058
author: Andreas Pomp
published in: Lecture Notes in Mathematics
publication date: 1998-04-27T00:00:00Z
review text: Beside the finite element method (FEM), the integral equation methods meet an increasing success to approximate the solutions of partial differential equations. A first kind of integral equation methods is given by the boundary element methods (BEM). Since they require the knowledge of a fundamental solution, their use in the approximation of general thin shell equations is quite difficult, or even impossible. This book studies a nice alternative, named ``boundary-domain integral method'' (BDIM) which couples boundary and domain integral equations and which can handle variable coefficients like in general thin shell equations. The aim of this book is to give a strong mathematical foundation of the BDIM from a numerical point of view and a detailed description of the complete algorithm. The contents can be summarized as follows: Part I (3 chapters) is dedicated to the construction of Levi functions of arbitrary degree of elliptic systems of partial differential equations with variable coefficients. Part II (4 chapters) considers the application of the general theory to the Donnell-Vlasov shell model. This model includes shells with a smooth and arbitrary curved mid-surface, the boundary of which may have corners. From this book, three main results can be retained: i) the algorithm to construct Levi functions; ii) the analysis of the order of error estimates (Theorem 6.10.1); iii) the discussion about the numerical effectiveness of BDIM and the comparison with FEM. This short monograph (163 pages) is attractive and nicely written and should be a brilliant alternative to more classical BEM approaches. Potential interested readers are applied mathematicians (mainly) and computational mechanicians at PhD level.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 74S15
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1146676
zbMATH Keywords: Donnell-Vlasov shell equations
zbMATH Keywords: boundary-domain integral method
zbMATH Keywords: finite element method
zbMATH Keywords: boundary element methods
zbMATH Keywords: thin shell equations
zbMATH Keywords: Levi functions
zbMATH Keywords: elliptic systems
zbMATH Keywords: algorithm
zbMATH Keywords: error estimate
zbMATH Keywords: monography
reviewed by: Michel Bernadou
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0094576
OpenAlex ID: W351556940
DOI: 10.1007/BFB0094576
description: scientific article; zbMATH DE number 1146676