# A C1-P2 finite element without nodal basis

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

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

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topZhang, 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 -

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