Adaptive finite element methods for elliptic equations over hierarchical T-meshes

DOI10.1016/j.cam.2011.05.016zbMath1231.65222OpenAlexW2067785421MaRDI QIDQ651929

Qiang Du, Li Tian, Falai Chen

Publication date: 19 December 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.05.016

zbMATH Keywords

numerical experimentselliptic equationspolynomial splinesa posteriori error estimationsadaptive finite elementnon-uniform rational B-splineshierarchical T-meshes

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (17)

A survey on the local refinable splines ⋮ On the dimension of spline spaces over T-meshes with smoothing cofactor-conformality method ⋮ Spline spaces with mixed orders of continuity over T-meshes ⋮ Isogeometric analysis on implicit domains using weighted extended PHT-splines ⋮ Goal-adaptive isogeometric analysis with hierarchical splines ⋮ Mapped B-spline basis functions for shape design and isogeometric analysis over an arbitrary parameterization ⋮ Modified bases of PHT-splines ⋮ Simple a posteriori error estimators in adaptive isogeometric analysis ⋮ Modified PHT-splines ⋮ Approximation power of polynomial splines on \(T\)-meshes ⋮ Parametric mesh regularization for interpolatory shape design and isogeometric analysis over a mesh of arbitrary topology ⋮ Rectified unstructured T-splines with dynamic weighted refinement for improvement in geometric consistency and approximation convergence ⋮ Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis ⋮ Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling ⋮ Modified basis functions for MPHT-splines ⋮ Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes ⋮ \(C^2\) interpolation T-splines

Uses Software

• ISOGAT
• ALBERTA

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Shape optimal design using B-splines
• Isogeometric analysis using T-splines
• Adaptive isogeometric analysis by local \(h\)-refinement with T-splines
• A posteriori error estimates for finite volume approximations of elliptic equations on general surfaces
• Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis
• A feedback finite element method with a posteriori error estimation. I: The finite element method and some basic properties of the a posteriori error estimator
• Knot insertion from a blossoming point of view
• Application of Hill functions to two-dimensional plate problems
• The coupling of geometric descriptions and finite elements using NURBs - A study in shape optimization
• Design of adaptive finite element software. The finite element toolbox ALBERTA. With CD-ROM
• Dimensions of spline spaces over T-meshes
• Isogeometric analysis of the Cahn-Hilliard phase-field model
• Local a posteriori estimates for pointwise gradient errors in finite element methods for elliptic problems
• A Posteriori Error Analysis of Finite Element Solutions for One-Dimensional Problems
• A‐posteriori error estimates for the finite element method
• Error Estimates for Adaptive Finite Element Computations
• Bicubic fundamental splines in plate bending
• All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Adaptive Finite Element Methods for Elliptic PDEs Based on Conforming Centroidal Voronoi–Delaunay Triangulations
• ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES

This page was built for publication: Adaptive finite element methods for elliptic equations over hierarchical T-meshes