The method of fundamental solutions for inhomogeneous elliptic problems
type: Item
instance of: scholarly article
title: The method of fundamental solutions for inhomogeneous elliptic problems
zbMATH Open document ID: 0913.65103
published in: Computational Mechanics
publication date: 1999-06-10T00:00:00Z
review text: Using some particular solutions of the Poisson equation or the inhomogeneous biharmonic equation, the authors transform the corresponding problems to homogeneous problems. Then they use the fundamental solutions to enforce the boundary conditions. These are satisfied in a least squares sense, namely by minimizing a nonlinear functional depending upon the unknown coefficients of the linear combination of fundamental solutions and the unknown coordinates of the sources points. However, the paper contains little discussion on any of the main topics in the numerical solution of partial differential equations, such as convergence of the discretized solution to the continuous solution, numerical stability of the computational algorithm, and error estimates of numerical solution.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 31A10
zbMATH DE Number: 1240671
zbMATH Keywords: method of fundamental solutions
zbMATH Keywords: Poisson equation
zbMATH Keywords: biharmonic equation
author: A. Poullikkas
author: A. Karageorghis
author: Georgios C. Georgiou
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: s004660050344
OpenAlex ID: W2123328754
DOI: 10.1007/S004660050344
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description: scientific article; zbMATH DE number 1240671