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Title: Are Bilinear Quadrilaterals Better Than Linear Triangles?

Abstract

This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear interpolation over quadrilaterals. For approximating a convex function, although bilinear quadrilaterals are more efficient, linear triangles are more accurate and may be preferred in finite element computations; whereas for saddle-shaped functions, quadrilaterals may offer a higher order approximation on a well-designed mesh. A surprising finding is different grid orientations may yield an order of magnitude improvement in approximation accuracy.

Authors:
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
OFFICE OF ENERGY RESEARCH, DOE (US)
OSTI Identifier:
814567
Report Number(s):
ORNL/TM-12388
TRN: US200318%%55
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 1 Jan 1993
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCURACY; INTERPOLATION; TRANSFORMATIONS

Citation Formats

D'Azevedo, E F. Are Bilinear Quadrilaterals Better Than Linear Triangles?. United States: N. p., 1993. Web. doi:10.2172/814567.
D'Azevedo, E F. Are Bilinear Quadrilaterals Better Than Linear Triangles?. United States. https://doi.org/10.2172/814567
D'Azevedo, E F. 1993. "Are Bilinear Quadrilaterals Better Than Linear Triangles?". United States. https://doi.org/10.2172/814567. https://www.osti.gov/servlets/purl/814567.
@article{osti_814567,
title = {Are Bilinear Quadrilaterals Better Than Linear Triangles?},
author = {D'Azevedo, E F},
abstractNote = {This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear interpolation over quadrilaterals. For approximating a convex function, although bilinear quadrilaterals are more efficient, linear triangles are more accurate and may be preferred in finite element computations; whereas for saddle-shaped functions, quadrilaterals may offer a higher order approximation on a well-designed mesh. A surprising finding is different grid orientations may yield an order of magnitude improvement in approximation accuracy.},
doi = {10.2172/814567},
url = {https://www.osti.gov/biblio/814567}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 1993},
month = {Fri Jan 01 00:00:00 EST 1993}
}