Implementation of continuous \(hp\)-adaptive finite element spaces without limitations on hanging sides and distribution of approximation orders

DOI10.1016/j.camwa.2015.06.033zbMath1443.65323OpenAlexW908954066MaRDI QIDQ2006250

Sônia M. Gomes, Jorge L. Díaz Calle, Philippe Remy Bernard Devloo

Publication date: 8 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2015.06.033

zbMATH Keywords

object oriented programming\(hp\)-adaptivity\(H^1\)-conforming finite elements

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (10)

Two dimensional mixed finite element approximations for elliptic problems with enhanced accuracy for the potential and flux divergence ⋮ A posteriori error estimator for a multiscale hybrid mixed method for Darcy's flows ⋮ A posteriori error estimates for primal hybrid finite element methods applied to Poisson problem ⋮ A semi‐hybrid‐mixed method for Stokes–Brinkman–Darcy flows with H(div)‐velocity fields ⋮ Exact sequences of conforming finite element spaces with interface constraints for macro polytopal meshes ⋮ Two-dimensional \(hp\) adaptive finite element spaces for mixed formulations ⋮ High-order composite finite element exact sequences based on tetrahedral-hexahedral-prismatic-pyramidal partitions ⋮ Hierarchical high order finite element bases for \(\mathbf{H}(\operatorname{div})\) spaces based on curved meshes for two-dimensional regions or manifolds ⋮ Three dimensional hierarchical mixed finite element approximations with enhanced primal variable accuracy ⋮ NeoPZ

Uses Software

• HP90
• deal.ii
• ParaView
• libMesh
• GitHub

Cites Work

• Systematic and generic construction of shape functions for \(p\)-adaptive meshes of multidimensional finite elements
• Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure
• Toward a universal h-p adaptive finite element strategy. II: A posteriori error estimation
• Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes
• The h-p version of the finite element method. I. The basic approximation results
• The h-p version of the finite element method. II. General results and applications
• An h-p adaptive finite element method for the numerical simulation of compressible flow
• Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers
• HP90: A general and flexible Fortran 90 \(hp\)-FE code
• A fully automatic \(hp\)-adaptivity
• The h, p and h-p versions of the finite element method in 1 dimension. III. The adaptive h-p version
• The \(hp\) finite element method for problems in mechanics with boundary layers
• Data structures and requirements for hp finite element software
• deal.II—A general-purpose object-oriented finite element library
• Error Estimates for Adaptive Finite Element Computations
• Computing with hp-ADAPTIVE FINITE ELEMENTS

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