An approximation method for the hypersingular heat operator equation
type: Item
instance of: scholarly article
title: An approximation method for the hypersingular heat operator equation
zbMATH Open document ID: 0942.65116
DOI: 10.1016/S0377-0427(99)00301-5
author: Martti Hamina
published in: Journal of Computational and Applied Mathematics
publication date: 2000-08-24T00:00:00Z
review text: Starting with the 2D equation of heat conductivity with zero initial data and Neumann boundary conditions, the author studies a numerical method for solving the related boundary integral formulation that is a hypersingular integral equation. The method, which can be interpreted as a Petrov-Galerkin scheme, uses tensor products of cubic splines in space and linear splines in time. In opposite to other methods known from the literature, the approximation here relies upon a collocation in space and not upon a boundary element method. Stability analysis and suboptimal convergence is provided for the case the spatial domain is a disk.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 1423320
zbMATH Keywords: hypersingular heat operator equation
zbMATH Keywords: boundary integral method
zbMATH Keywords: Petrov-Galerkin method
zbMATH Keywords: stability
zbMATH Keywords: hypersingular integral equation
zbMATH Keywords: collocation
zbMATH Keywords: convergence
reviewed by: Etienne Emmrich
MaRDI profile type: Publication
cites work: On the Asymptotic Convergence of Collocation Methods
cites work: Boundary integral operators for the heat equation
cites work: Spline collocation for convolutional parabolic boundary integral equations
cites work: Q3736253
cites work: Q4397028
cites work: Q3837906
cites work: Q3837907
cites work: Q4846892
cites work: On the Spline Collocation Method for the Single-Layer Heat Operator Equation
cites work: Boundary integral solution of the two-dimensional heat equation
cites work: Q5628582
cites work: Q5634306
description: scientific article; zbMATH DE number 1423320