Splines on Triangulations with Hanging Vertices

被引：8

作者：

Schumaker, Larry L. ^{[1
]}

Wang, Lujun ^{[1
]}

机构：

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

来源：

CONSTRUCTIVE APPROXIMATION | 2012年 / 36卷 / 03期

关键词：

Splines; Triangulations; H-triangulations; Hanging nodes; Dimension; Approximation power;

D O I：

10.1007/s00365-012-9167-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Polynomial spline spaces defined on triangulations with hanging vertices are studied. In addition to dimension formulae, explicit basis functions are constructed, and their supports and stability are discussed. The approximation power of the spaces is also treated.

引用

页码：487 / 511

页数：25

共 8 条

[1]

Ainsworth M., 2000, PUR AP M-WI

[2] A multilevel preconditioner for the interior penalty discontinuous Galerkin method [J].

Brix, Kolja ;

Pinto, Martin Campos ;

Dahmen, Wolfgang .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 46 (05) :2742-2768

[3]

Lai M., 2007, Spline functions on triangulations, Encyclopedia of Mathematics and its Applications

[4] Dual bases for spline spaces on cells [J].

Schumaker, Larry L. .

Computer Aided Geometric Design, 1988, 5 (04) :277-284

[5]

Schumaker L.L., 1979, Multivariate Approx. Theory, P396

[6] Computing bivariate splines in scattered data fitting and the finite-element method [J].

Schumaker, Larry L. .

NUMERICAL ALGORITHMS, 2008, 48 (1-3) :237-260

[7] Spline spaces on TR-meshes with hanging vertices [J].

Schumaker, Larry L. ;

Wang, Lujun .

NUMERISCHE MATHEMATIK, 2011, 118 (03) :531-548

[8] Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM [J].

Solin, Pavel ;

Cerveny, Jakub ;

Dolezel, Ivo .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2008, 77 (01) :117-132

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