Gradient Bounds for Wachspress Coordinates on Polytopes [PDF]
SIAM Journal on Numerical Analysis, 2014 We derive upper and lower bounds on the gradients of Wachspress coordinates defined over any simple convex d-dimensional polytope P. The bounds are in terms of a single geometric quantity h_*, which denotes the minimum distance between a vertex of P and any hyperplane containing a non-incident face.
N Sukumar, Andrew Gillette
exaly +3 more sources
Projective Geometry of Wachspress Coordinates [PDF]
Foundations of Computational Mathematics, 2019 Abstract We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane arrangement. This generalizes the construction of the adjoint curve of a polygon by Wachspress (A rational finite element basis, Academic Press, New York, 1975).
Kathlen Köhn +2 more
exaly +6 more sources
Convergence of Wachspress coordinates: from polygons to curved domains [PDF]
Advances in Computational Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael Barton, Jiří Kosinka
exaly +4 more sources
Extension of Dasgupta’s Technique for Higher Degree Approximation
Universitas Scientiarum, 2021 In the present paper, rational wedge functions for degree two approximation have been computed over a pentagonal discretization of the domain, by using an analytic approach which is an extension of Dasgupta’s approach for linear approximation.
P. L. Powar +2 more
doaj +1 more source
Upper bound of high-order derivatives for Wachspress coordinates on polytopes
CoRRThe gradient bounds of generalized barycentric coordinates play an essential role in the $H^1$ norm approximation error estimate of generalized barycentric interpolations. Similarly, the $H^k$ norm, $k>1$, estimate needs upper bounds of high-order derivatives, which are not available in the literature.
Pengjie Tian, Yanqiu Wang
openaire +2 more sources
Vertex Displacement-Based Discontinuous Deformation Analysis Using Virtual Element Method. [PDF]
Materials (Basel), 2021 Luo H, Sun G, Liu L, Jiang W.
europepmc +1 more source
Functional Data Approximation on Bounded Domains using Polygonal Finite Elements. [PDF]
Comput Aided Geom Des, 2018 Cao J, Xiao Y, Chen Z, Wang W, Bajaj C.
europepmc +1 more source
CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES. [PDF]
J Comput Methods Appl Math, 2016 Gillette A, Rand A, Bajaj C.
europepmc +1 more source
Error Estimates for Generalized Barycentric Interpolation. [PDF]
Adv Comput Math, 2012 Gillette A, Rand A, Bajaj C.
europepmc +1 more source
Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons. [PDF]
Adv Comput Math, 2013 Rand A, Gillette A, Bajaj C.
europepmc +1 more source