A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method
From MaRDI portal
Publication:3549790
DOI10.1002/nme.2515zbMath1183.74259OpenAlexW2145320987MaRDI QIDQ3549790
Éric Béchet, Nicolas Moës, Barbara I. Wohlmuth
Publication date: 29 March 2010
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.2515
Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
Related Items
Application of an enriched FEM technique in thermo-mechanical contact problems ⋮ Large deformation frictional contact analysis with immersed boundary method ⋮ Three-dimensional numerical modelling by XFEM of spring-layer imperfect curved interfaces with applications to linearly elastic composite materials ⋮ Stabilized global-local X-FEM for 3D non-planar frictional crack using relevant meshes ⋮ A level-set-based large sliding contact algorithm for easy analysis of implant positioning ⋮ Robust imposition of Dirichlet boundary conditions on embedded surfaces ⋮ A weighted Nitsche's method for interface problems with higher-order simplex elements ⋮ An Extended Finite Element Method for the Analysis of Submicron Heat Transfer Phenomena ⋮ A generalized multigrid method for solving contact problems in Lagrange multiplier based unfitted finite element method ⋮ A barrier method for frictional contact on embedded interfaces ⋮ Stabilized method of imposing Dirichlet boundary conditions using a recovered stress field ⋮ A non-overlapping domain decomposition method with perfectly matched layer transmission conditions for the Helmholtz equation ⋮ An ``immersed finite element method based on a locally anisotropic remeshing for the incompressible Stokes problem ⋮ An embedded mesh method for treating overlapping finite element meshes ⋮ Large sliding contact along branched discontinuities with X-FEM ⋮ A study on unfitted 1D finite element methods ⋮ A weighted Nitsche stabilized method for small-sliding contact on frictional surfaces ⋮ A coupled Eulerian-Lagrangian extended finite element formulation for simulating large deformations in hyperelastic media with moving free boundaries ⋮ A NURBS enhanced extended finite element approach for unfitted CAD analysis ⋮ Impact on highly compressible media in explicit dynamics using the X-FEM ⋮ 3D crack propagation with cohesive elements in the extended finite element method ⋮ Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods ⋮ A stable extended FEM formulation for multi-phase problems enforcing the accuracy of the fluxes through Lagrange multipliers ⋮ Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers ⋮ Interface problems with quadratic X-FEM: design of a stable multiplier space and error analysis ⋮ A high-order immersed boundary discontinuous-Galerkin method for Poisson's equation with discontinuous coefficients and singular sources ⋮ Explicit dynamics with a non-local damage model using the thick level set approach ⋮ A new formulation for imposing Dirichlet boundary conditions on non-matching meshes ⋮ An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects ⋮ A particle-based moving interface method (PMIM) for modeling the large deformation of boundaries in soft matter systems ⋮ A computational approach based on extended finite element method for thin porous layers in acoustic problems ⋮ A dual mortar embedded mesh method for internal interface problems with strong discontinuities ⋮ On the Use of Anisotropic Triangles with Mixed Finite Elements: Application to an “Immersed” Approach for Incompressible Flow Problems ⋮ A Multi-Dimensional Lagrange Multiplier Method to Identify the Load Distribution on 3D Special-Shaped Surface in the Strength Analysis of Aircraft Structure ⋮ A Nitsche embedded mesh method ⋮ A global model reduction approach for 3D fatigue crack growth with confined plasticity ⋮ Finite element analysis on implicitly defined domains: an accurate representation based on arbitrary parametric surfaces ⋮ An efficient preconditioner for monolithically-coupled large-displacement fluid-structure interaction problems with pseudo-solid mesh updates ⋮ A local projection stabilization of fictitious domain method for elliptic boundary value problems ⋮ A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part II: Intersecting interfaces ⋮ Stabilized low-order finite elements for frictional contact with the extended finite element method ⋮ Fictitious domain finite element methods using cut elements. I: A stabilized Lagrange multiplier method ⋮ Numerical modeling of corrosion pit propagation using the combined extended finite element and level set method ⋮ ILS-MPM: an implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles ⋮ A stable extended/generalized finite element method with Lagrange multipliers and explicit damage update for distributed cracking in cohesive materials ⋮ Optimal convergence analysis for the extended finite element method ⋮ Robust and scalable \(h\)-adaptive aggregated unfitted finite elements for interface elliptic problems ⋮ A kd-tree-accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data ⋮ An embedded mesh method in a multiple material ALE ⋮ A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis ⋮ 3D coupled HM-XFEM modeling with cohesive zone model and applications to non planar hydraulic fracture propagation and multiple hydraulic fractures interference ⋮ A variational multiscale immersed meshfree method for heterogeneous materials ⋮ A stabilized finite element method for enforcing stiff anisotropic cohesive laws using interface elements ⋮ Projection stabilization of Lagrange multipliers for the imposition of constraints on interfaces and boundaries ⋮ A multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within XFEM ⋮ A mortar-type finite element approach for embedding 1D beams into 3D solid volumes ⋮ A robust Nitsche's formulation for interface problems ⋮ A multi-model X-FEM strategy dedicated to frictional crack growth under cyclic fretting fatigue loadings ⋮ Effective conductivity of a composite material with stiff imperfect contact conditions ⋮ XFEM-Based Fictitious Domain Method for Linear Elasticity Model with Crack ⋮ Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery ⋮ The thick level set method: sliding deformations and damage initiation ⋮ Anisotropic mesh adaptation with optimal convergence for finite elements using embedded geometries ⋮ A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. I: Single interface ⋮ The virtual element method for rock mass with frictional cracks ⋮ A finite element framework for modeling internal frictional contact in three-dimensional fractured media using unstructured tetrahedral meshes ⋮ A weak penalty formulation remedying traction oscillations in interface elements ⋮ Numerical modelling of electromechanical coupling using fictitious domain and level set methods ⋮ A modified perturbed Lagrangian formulation for contact problems ⋮ Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes ⋮ On the use of the extended finite element method with quadtree/octree meshes ⋮ An X-FEM and level set computational approach for image-based modelling: Application to homogenization ⋮ A mesh adaptation procedure for periodic domains
Cites Work
- Imposing essential boundary conditions in mesh-free methods
- Residual-free bubbles for embedded Dirichlet problems
- A mortared finite element method for frictional contact on arbitrary interfaces
- A formulation for frictionless contact problems using a weak form introduced by Nitsche
- The finite element method with Lagrange multipliers on the boundary: Circumventing the Babuška-Brezzi condition
- The partition of unity finite element method: basic theory and applications
- A computational approach to handle complex microstructure geometries.
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- On some techniques for approximating boundary conditions in the finite element method
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
- Arbitrary discontinuities in finite elements
- Partition of unity-based discontinuous elements for interface phenomena: computational issues
- The inf-sup test
- A bubble-stabilized finite element method for Dirichlet constraints on embedded interfaces
- Mixed and Hybrid Finite Element Methods
- Elastic crack growth in finite elements with minimal remeshing
- Extended finite element method for three-dimensional crack modelling
- Arbitrary branched and intersecting cracks with the extended finite element method
- Non-planar 3D crack growth by the extended finite element and level sets-Part I: Mechanical model
- A finite element method for crack growth without remeshing
- On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method
- Modeling holes and inclusions by level sets in the extended finite element method
- An extended finite element method for modeling crack growth with frictional contact.