Two-dimensional mesh embedding for B-spline methods
type: Item
instance of: scholarly article
title: Two-dimensional mesh embedding for B-spline methods
zbMATH Open document ID: 0910.65083
author: Karim Shariff
author: Robert D. Moser
published in: Journal of Computational Physics
publication date: 1999-04-09T00:00:00Z
review text: A technique is developed for achieving a two-dimensional mesh embedding with B-splines as basis function. An algorithm is provided for generating a spline basis, where the domain is partitioned into arbitrary rectangles. The spline basis automatically has the same high degree of continuity (\(C^{d-1}\), where \(d\) is the polynomial degree) at zonal boundaries as everywhere else. The basis functions are simply a suitable product of one-dimensional B-splines. Both integer and noninteger refinement ratios are allowed across the mesh blocks. The basis may be used to form differential operators using a Galerkin or collocation scheme. Test cases for linear scalar equations such as the Poisson and advection equation are presented. \(\copyright\) Academic Press.
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65N35
zbMATH DE Number: 1212301
zbMATH Keywords: B-splines
zbMATH Keywords: mesh embedding
zbMATH Keywords: Galerkin methods
zbMATH Keywords: Poisson equation
zbMATH Keywords: collocation
zbMATH Keywords: advection equation
reviewed by: Karel Najzar
MaRDI profile type: Publication
full work available at URL: jcph.1998.6053
OpenAlex ID: W1994386855
cites work: Zonal embedded grids for numerical simulations of wall-bounded turbulent flows
cites work: Compact finite difference schemes with spectral-like resolution
cites work: Q4765962
cites work: An h-p adaptive finite element method for the numerical simulation of compressible flow
cites work: Numerical treatment of grid interfaces for viscous flows
cites work: A practical guide to splines
cites work: Q4404383
cites work: Q4053037
cites work: On Compactly Supported Spline Wavelets and a Duality Principle
DOI: 10.1006/JCPH.1998.6053
description: scientific article; zbMATH DE number 1212301