Spline functions on triangulations
By Ming-Jun Lai, L. Schumaker. Encyclopedia of mathematics and its applications, 2007
557 citations recorded by the source corpus.
Subfields: Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/020dc250dd0136eb57882c233fc185f2405db862
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- L. Beirão da Veiga
- Giancarlo Sangalli
- Rafael Vázquez Hernández
- Annalisa Buffa
- Li Wang
- Jingru Mu
- Guannan Wang
- Ming-Jun Lai
Citations in the corpus
- Estimation and inference in spatially varying coefficient models (2018, methodology): “Our method tackles the estimation problem differently from the local approach, and the coefficient functions 𝛽k(·) are approximated using the bivariate splines over triangulations (BSTs) by Lai and Schumaker (2007) and Lai and Wang (2013).”
- A locking-free model for Reissner-Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS (2015, unknown): “, [20]).”
- A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C1 rational triangular Bézier spline discretizations (2018, unknown): “From the virtual work equation (ie, Equation (27)), we obtain the stiffness K and forcing terms F, ie,”
- Mathematical analysis of variational isogeometric methods* (2014, background): “Furthermore, splines can be defined over triangulations (see Lai and Schumaker 2007 and the references therein), but the construction cannot easily be extended to three space dimensions.”
- Bivariate Penalized Splines for Regression (2013, background): “One could also use a degree d < 5 for r = 1 if the triangulation △ is special; see a summary of special triangulations in Lai and Schumaker (2007).”
- Spatial spline regression models (2013, unknown): “…Guillas and Lai (2010) consider a regularizing term involving linear combinations of all partial derivatives up to a chosen order, and employ bivariate splines over triangulations (see, e.g., Lai and Schumaker 2007), that, likewise finite elements, provide a basis for piecewise-polynomial surfaces.”