0000000000015790

AUTHOR

Alexei Lozinski

showing 2 related works from this author

Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three

2020

International audience; We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case.

010103 numerical & computational mathematicsResidual01 natural sciencesPiecewise linear function: Multidisciplinaire généralités & autres [C99] [Ingénierie informatique & technologie]Dimension (vector space)Bank-Weiser estimatorApplied mathematicsfinite element methodssaturation assumption0101 mathematicsReliability (statistics)Mathematicsresidual estimatorBank-WeiserestimatorApplied Mathematics: Multidisciplinary general & others [C99] [Engineering computing & technology]NoveltyEstimatorExtension (predicate logic)16. Peace & justiceFinite element methoda posteriori error estimation010101 applied mathematics: Mathematics [G03] [Physical chemical mathematical & earth Sciences]: Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre][MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
researchProduct

Computing bi-tangents for transmission belts

2020

In this note, we determine the bi-tangents of two rotated ellipses, and we compute the coordinates of their points of tangency. For these purposes, we develop two approaches. The first one is an analytical approach in which we compute analytically the equations of the bi-tangents. This approach is valid only for some cases. The second one is geometrical and is based on the determination of the normal vector to the tangent line. This approach turns out to be more robust than the first one and is valid for any configuration of ellipses.

bi-tangentsanalytical approach[MATH] Mathematics [math][MATH]Mathematics [math]rotated ellipsesgeometrical approach
researchProduct