Hanging nodes and XFEM

DOI10.1002/nme.3024zbMath1216.74020OpenAlexW2036559973MaRDI QIDQ3006539

Andreas Schröder, Alaskar Alizada, Thomas-Peter Fries, Kwok Wah Cheng, Andreas Byfut

Publication date: 20 June 2011

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.3024

zbMATH Keywords

interfacerefinementXFEMhanging nodes1-irregular

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items

A two-scale generalized finite element method for fatigue crack propagation simulations utilizing a fixed, coarse hexahedral mesh, XFEM‐based element subscale refinement for detailed representation of crack propagation in large‐scale analyses, An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems, hp-adaptive extended finite element method, Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description, Convergence estimates for multigrid algorithms with SSC smoothers and applications to overlapping domain decomposition, Deforming fluid domains within the finite element method: five mesh-based tracking methods in comparison, Structured mesh refinement in MLS-based numerical manifold method and its application to crack problems, Efficient analysis of transient heat transfer problems exhibiting sharp thermal gradients, Modeling and simulation of kinked cracks by virtual node XFEM, Efficient methods for implicit geometrical representation of complex material microstructures, A finite element method with mesh-separation-based approximation technique and its application in modeling crack propagation with adaptive mesh refinement, An adaptive interface-enriched generalized FEM for the treatment of problems with curved interfaces, A polytree-based adaptive scheme for modeling linear fracture mechanics using a coupled XFEM-SBFEM approach, Automatic image-based analyses using a coupled quadtree-SBFEM/SCM approach, Construction of H-Refined Continuous Finite Element Spaces with Arbitrary Hanging Node Configurations and Applications to Multigrid Algorithms, Computational methods for fracture in brittle and quasi-brittle solids: state-of-the-art review and future perspectives, Robust modelling of implicit interfaces by the scaled boundary finite element method, Local refinement with arbitrary irregular meshes and implementation in numerical manifold method, An adaptive concurrent multiscale method for microstructured elastic solids, XFEM with hanging nodes for two-phase incompressible flow, A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model, Loaded crack surfaces in two and three dimensions with XFEM, Finite element computations over quadtree meshes: strain smoothing and semi-analytical formulation, An improved multigrid algorithm for \(n\)-irregular meshes with subspace correction smoother, Multi-level \(hp\)-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes, Forward modelling of geophysical electromagnetic data on unstructured grids using an adaptive mimetic finite-difference method, A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials, Crack analysis using numerical manifold method with strain smoothing technique and corrected approximation for blending elements, A one-field monolithic fictitious domain method for fluid-structure interactions, A new three-level mesh method to accelerate the structural topology optimization

Uses Software

• XFEM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Modeling thermal fatigue cracking in integrated circuits by level sets and the extended finite element method
• Piecewise polynomial shape functions for \(hp\)-finite element methods
• Derivative recovery and a posteriori error estimate for extended finite elements
• Modelling of cohesive crack growth in concrete structures with the extended finite element method
• Analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes
• On spurious velocities in incompressible flow problems with interfaces
• Energy-based modeling of cohesive and cohesionless cracks via X-FEM
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements
• Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers
• A level set approach for computing solutions to incompressible two-phase flow
• A computational approach to handle complex microstructure geometries.
• Arbitrary-level hanging nodes and automatic adaptivity in the \(hp\)-FEM
• An improved interface element with variable nodes for non-matching finite element meshes
• Arbitrary discontinuities in finite elements
• Modelling crack growth by level sets in the extended finite element method
• hp-adaptive extended finite element method
• On time integration in the XFEM
• MLS-based variable-node elements compatible with quadratic interpolation. Part I: formulation and application for non-matching meshes
• A front remeshing technique for a Lagrangian description of moving interfaces in two-fluid flows
• Higher-order XFEM for curved strong and weak discontinuities
• The XFEM for high-gradient solutions in convection-dominated problems
• An extended finite element library
• A corrected XFEM approximation without problems in blending elements
• A recovery-type error estimator for the extended finite element method based onsingular+smoothstress field splitting
• A posteriorierror estimation for extended finite elements by an extended global recovery
• Parametric enrichment adaptivity by the extended finite element method
• The intrinsic XFEM for two-fluid flows
• A finite element for transition from a fine to a coarse grid
• Elastic crack growth in finite elements with minimal remeshing
• On the construction of blending elements for local partition of unity enriched finite elements
• New crack‐tip elements for XFEM and applications to cohesive cracks
• Arbitrary branched and intersecting cracks with the extended finite element method
• XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials
• A new 3D finite element for adaptive h‐refinement in 1‐irregular meshes
• A finite element method for crack growth without remeshing
• A simple error estimator for extended finite elements
• High-order extended finite element method for cracked domains
• Level set methods: An overview and some recent results
• Modeling holes and inclusions by level sets in the extended finite element method