On some boundary element methods for the heat equation
type: Item
instance of: scholarly article
title: On some boundary element methods for the heat equation
zbMATH Open document ID: 0584.65076
DOI: 10.1007/BF01400258
author: B. George
published in: Numerische Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/132985
review text: The Dirichlet problem and the Neumann problem for the heat equation in one space dimension with given initial values are considered. In the first approach the boundary integral equation based on the heat equation is approximately solved by a piecewise constant ansatz for the normal derivative in the Dirichlet problem, by a piecewise linear ansatz for the boundary values of the solution of the differential equation in the Neumann problem (discretization by a constant time-step). The approximate solution is then obtained by aid of the integral representation. In the second approach the boundary element technique is applied to the set of elliptic problems arising from discretization of the heat equation in time. The convergence analysis is carried out for both approaches.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 3936433
zbMATH Keywords: heat potential
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Neumann problem
zbMATH Keywords: boundary integral equation
zbMATH Keywords: convergence
reviewed by: Rudolf Gorenflo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3936433