A C1-P2 finite element without nodal basis

Shangyou Zhang

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 2, page 175-192
  • ISSN: 0764-583X

Abstract

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A new finite element, which is continuously differentiable, but only piecewise quadratic polynomials on a type of uniform triangulations, is introduced. We construct a local basis which does not involve nodal values nor derivatives. Different from the traditional finite elements, we have to construct a special, averaging operator which is stable and preserves quadratic polynomials. We show the optimal order of approximation of the finite element in interpolation, and in solving the biharmonic equation. Numerical results are provided confirming the analysis.


How to cite

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Zhang, Shangyou. "A C1-P2 finite element without nodal basis." ESAIM: Mathematical Modelling and Numerical Analysis 42.2 (2008): 175-192. <http://eudml.org/doc/250367>.

@article{Zhang2008,
abstract = {
A new finite element, which is continuously differentiable, but only piecewise quadratic polynomials on a type of uniform triangulations, is introduced. We construct a local basis which does not involve nodal values nor derivatives. Different from the traditional finite elements, we have to construct a special, averaging operator which is stable and preserves quadratic polynomials. We show the optimal order of approximation of the finite element in interpolation, and in solving the biharmonic equation. Numerical results are provided confirming the analysis.
},
author = {Zhang, Shangyou},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Differentiable finite element; quadratic element; biharmonic equation; Strang's conjecture; criss-cross grid; averaging interpolation; non-derivative basis.; differentiable finite element; biharmonic equation; criss-cross grid; non-derivative basis; stability; numerical results},
language = {eng},
month = {3},
number = {2},
pages = {175-192},
publisher = {EDP Sciences},
title = {A C1-P2 finite element without nodal basis},
url = {http://eudml.org/doc/250367},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Zhang, Shangyou
TI - A C1-P2 finite element without nodal basis
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/3//
PB - EDP Sciences
VL - 42
IS - 2
SP - 175
EP - 192
AB - 
A new finite element, which is continuously differentiable, but only piecewise quadratic polynomials on a type of uniform triangulations, is introduced. We construct a local basis which does not involve nodal values nor derivatives. Different from the traditional finite elements, we have to construct a special, averaging operator which is stable and preserves quadratic polynomials. We show the optimal order of approximation of the finite element in interpolation, and in solving the biharmonic equation. Numerical results are provided confirming the analysis.

LA - eng
KW - Differentiable finite element; quadratic element; biharmonic equation; Strang's conjecture; criss-cross grid; averaging interpolation; non-derivative basis.; differentiable finite element; biharmonic equation; criss-cross grid; non-derivative basis; stability; numerical results
UR - http://eudml.org/doc/250367
ER -

References

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