Optimal convergence analysis for the extended finite element method
From MaRDI portal
Publication:3006545
DOI10.1002/nme.3092zbMath1216.74029OpenAlexW1987575497MaRDI QIDQ3006545
Serge Nicaise, Elie Chahine, Yves Renard
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.3092
Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) 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
Algorithm for Processing the Results of Calculations for Determining the Body of Optimal Parameters in the Weighted Finite Element Method, An explicit residual-type error estimator for Q1-quadrilateral extended finite element method in two-dimensional linear elastic fracture mechanics, Nonconforming immersed finite element method for solving elliptic optimal control problems with interfaces, An automated mesh generation algorithm for simulating complex crack growth problems, Error estimate FEM for the Nikol'skij-Lizorkin problem with degeneracy, Stable generalized finite element method (SGFEM) for three-dimensional crack problems, Stable generalized finite element method and associated iterative schemes; application to interface problems, The eXtended finite element method for cracked hyperelastic materials: A convergence study, CutFEM: Discretizing geometry and partial differential equations, Condensed generalized finite element method, DOF‐gathering stable generalized finite element methods for crack problems, A non-conformal extended finite element approach: integral matching Xfem, Weighted finite element method and body of optimal parameters for elasticity problem with singularity, A stabilized Lagrange multiplier method for the enriched finite-element approximation of Tresca contact problems of cracked elastic bodies, A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics, The hydromechanical equilibrium state of poroelastic media with a static fracture: A dimension-reduced model with existence results in weighted Sobolev spaces and simulations with an XFEM discretization, Extended finite element methods for optimal control problems governed by Poisson equation in non-convex domains, A Nitsche-extended finite element method for distributed optimal control problems of elliptic interface equations, Strongly stable generalized finite element method (SSGFEM) for a non-smooth interface problem, On the enrichment zone size for optimal convergence rate of the generalized/extended finite element method, XLME interpolants, a seamless bridge between XFEM and enriched meshless methods, An extended isogeometric thin shell analysis based on Kirchhoff-love theory, A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method, Robustness in stable generalized finite element methods (SGFEM) applied to Poisson problems with crack singularities, Error-controlled adaptive extended finite element method for 3D linear elastic crack propagation, Interface solutions of partial differential equations with point singularity, Extended HDG methods for second order elliptic interface problems, Unfitted extended finite elements for composite grids
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A non-conformal extended finite element approach: integral matching Xfem
- An asymptotic finite plane deformation analysis of the elastostatic fields at a notch vertex of an incompressible hyperelastic material
- On finite element methods for elliptic equations on domains with corners
- The partition of unity finite element method: basic theory and applications
- An extended finite element method with higher-order elements for curved cracks
- A finite element method for the simulation of strong and weak discontinuities in solid mechanics
- On the finite element method
- Superconvergent extraction of flux intensity factors and first derivatives from finite element solutions
- A substructured FE/XFE method for stress intensity factors computation in an industrial structure
- Improved implementation and robustness study of the X-FEM for stress analysis around cracks
- Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery
- X-FEM, de nouvelles frontières pour les éléments finis
- On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite-Element Method
- Error estimates on the coeficients obtained by the singular function method
- Spider XFEM, an extended finite element variant for partially unknown crack-tip displacement
- A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method
- A New Fictitious Domain Approach Inspired by the Extended Finite Element Method
- An extended finite element library
- A substructured FE-shell/XFE-3D method for crack analysis in thin-walled structures
- Crack tip enrichment in the XFEM using a cutoff function
- A Reduced Basis Enrichment for the eXtended Finite Element Method
- Sur une Interprétation Mathématique de l'Intégrale de Rice en Théorie de la Rupture Fragile
- Coefficients of the Singularities for Elliptic Boundary Value Problems on Domains with Conical Points. III: Finite Element Methods on Polygonal Domains
- A finite element method for crack growth without remeshing
- High-order extended finite element method for cracked domains
