General interior Hermite collocation methods for second-order elliptic partial differential equations
type: Item
instance of: scholarly article
title: General interior Hermite collocation methods for second-order elliptic partial differential equations
zbMATH Open document ID: 0817.65092
DOI: 10.1016/0168-9274(94)00055-7
author: Yu-Ling Lai
author: Elias N. Houstis
author: John R. Rice
author: A. Hadjidimos
published in: Applied Numerical Mathematics
publication date: 1995-08-13T00:00:00Z
full work available at URL: https://docs.lib.purdue.edu/cgi/viewcontent.cgi
review text: The paper discusses the iterative solution of linear systems resulting from the collocation based on \(C^ 1\)-piecewise polynomials for second- order elliptic partial differential equations on rectilinear regions. First it describes the code GENCOL for general cubic Hermit collocation in 2D domains and the simplified code GINCOL for rectilinear domains and uncoupled boundary conditions. Since the properties of the resulting collocation matrix strongly depends on the ordering of the unknowns and equations, two kinds of ordering schemes are discussed, the finite element and the tensor product ordering. It is shown that tensor product ordering produces linear systems suitable for block iterative solvers of overrelaxation and conjugate gradient type. A number of numerical experiments are reported that indicate the applicability and effectiveness of accelerated overrelaxation and conjugate gradient iterative schemes.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35-04
zbMATH DE Number: 721001
zbMATH Keywords: finite element ordering
zbMATH Keywords: second-order elliptic partial differential equations
zbMATH Keywords: code GENCOL
zbMATH Keywords: cubic Hermit collocation
zbMATH Keywords: ordering schemes
zbMATH Keywords: tensor product ordering
zbMATH Keywords: block iterative solvers
zbMATH Keywords: overrelaxation
zbMATH Keywords: conjugate gradient
zbMATH Keywords: numerical experiments
reviewed by: Gunther Schmidt
describes a project that uses: ELLPACK
MaRDI profile type: Publication
OpenAlex ID: W2055941941
cites work: Q4091004
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description: scientific article; zbMATH DE number 721001