Boundary element approach for an inverse source problem of the Poisson equation with a one-point-mass-like source
type: Item
instance of: scholarly article
title: Boundary element approach for an inverse source problem of the Poisson equation with a one-point-mass-like source
zbMATH Open document ID: 0810.65117
DOI: 10.1016/0307-904X(94)90084-1
author: Takashi Ohe
author: Kohzaburo Ohnaka
published in: Applied Mathematical Modelling
publication date: 1994-01-01T00:00:00Z
review text: The authors consider the problem of determining the source term \(f\) of a two-dimensional Poisson equation \(-\Delta u = f\) in a bounded convex domain, assuming the solution \(u\) and the flux given on the boundary. They discuss in detail the particular problem of finding the center \((a,b)\) of a radially symmetric source \(f(x,y) = F(r_{a,b})\), \(r^ 2_{a, b} = (x - a)^ 2 + (y - b)^ 2\), with \(a\) and \(b\) unknown. They eliminate the harmonic part of \(u\) by using boundary integral relations and propose an iterative algorithm for approximating the center. For approximation of the logarithmic potential \(u\) on the boundary they use the boundary element method and derive error estimates, under appropriate smoothness assumptions, for the case of piecewise constant ansatz. Finally, they demonstrate applicability of their method by displaying results of a numerical case study.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 622120
zbMATH Keywords: inverse source problem
zbMATH Keywords: boundary element method
zbMATH Keywords: elimination of harmonic term
zbMATH Keywords: error estimate
zbMATH Keywords: Poisson equation
zbMATH Keywords: numerical case study
reviewed by: Rudolf Gorenflo
MaRDI profile type: Publication
cites work: Q4002332
cites work: On the Uniqueness of the Inverse Logarithmic Potential Problem
cites work: Boundary element approach for identification of point forces of distributed parameter systems
cites work: Boundary element approach for identification of the external forces in the scalar wave equations
cites work: Q3219912
cites work: Q4060751
cites work: Asymptotic Expansions for Product Integration
description: scientific article; zbMATH DE number 622120