On the improvement of the triangular Shepard method by non conformal polynomial elements

DOI10.1016/j.apnum.2022.10.017OpenAlexW4308750299MaRDI QIDQ2106235

F. Di Tommaso, Federico Nudo, Allal Guessab, Francesco Dell'Accio

Publication date: 9 December 2022

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2022.10.017

zbMATH Keywords

nonconforming finite elementenriched finite element methodscattered data interpolationtriangular Shepard method

Mathematics Subject Classification ID

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Approximations and expansions (41Axx)

Related Items (3)

A unified enrichment approach of the standard three-node triangular element ⋮ A general class of enriched methods for the simplicial linear finite elements ⋮ Enrichment strategies for the simplicial linear finite elements

Uses Software

• Algorithm 792
• Triangle

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local numerical integration on the sphere
• Error estimates for modified local Shepard's interpolation formula
• The bivariate Shepard operator of Bernoulli type
• Increasing the approximation order of the triangular Shepard method
• A multivariate version of Hammer's inequality and its consequences in numerical integration
• Numerical integration using integrals over hyperplane sections of simplices in a triangulation of a polytope
• Nonconforming finite element methods
• Fast and accurate scattered Hermite interpolation by triangular Shepard operators
• Bivariate Shepard-Bernoulli operators
• An efficient trivariate algorithm for tetrahedral Shepard interpolation
• Fast computation of triangular Shepard interpolants
• How to Integrate a Polynomial over a Sphere
• On the approximation order of triangular Shepard interpolation
• Rate of Convergence of Shepard's Global Interpolation Formula
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• Shepard's Method of "Metric Interpolation" to Bivariate and Multivariate Interpolation
• Algorithm 792
• Extended Multidimensional Integration Formulas on Polytope Meshes
• A simple necessary and sufficient condition for the enrichment of the Crouzeix-Raviart element
• A Unified and General Framework for Enriching Finite Element Approximations
• Complete Hermite-Birkhoff interpolation on scattered data by combined Shepard operators

This page was built for publication: On the improvement of the triangular Shepard method by non conformal polynomial elements