RECENT DEVELOPMENT OF IMMERSED FEM FOR ELLIPTIC AND ELASTIC INTERFACE PROBLEMS

DOI10.12941/jksiam.2019.23.065zbMath1434.65260OpenAlexW3126911788MaRDI QIDQ5213116

Gwanghyun Jo, Do Young Kwak

Publication date: 31 January 2020

Full work available at URL: http://koasas.kaist.ac.kr:8080/handle/10203/267406

zbMATH Keywords

heterogeneous materialsmultigrid methodimmersed finite element methodelasticity problemsCrouzeix-Raviart finite elementtraction condition

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Second-order elliptic equations (35J15)

Related Items (6)

Discontinuous bubble immersed finite element method for Poisson-Boltzmann-Nernst-Planck model ⋮ Locally conservative immersed finite element method for elliptic interface problems ⋮ A moving kriging interpolation-based meshfree method for solving two-phase elasticity system ⋮ Construction of discontinuous enrichment functions for enriched or generalized FEM's for interface elliptic problems in 1D ⋮ High-Order Enriched Finite Element Methods for Elliptic Interface Problems with Discontinuous Solutions ⋮ A new immersed finite element method for two-phase Stokes problems having discontinuous pressure

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A locking-free immersed finite element method for planar elasticity interface problems
• Linear and bilinear immersed finite elements for planar elasticity interface problems
• A symmetric and consistent immersed finite element method for interface problems
• Discontinuous bubble scheme for elliptic problems with jumps in the solution
• A finite element method for interface problems in domains with smooth boundaries and interfaces
• Compatible algorithms for coupled flow and transport
• Optimal convergence analysis of an immersed interface finite element method
• Two families of mixed finite elements for second order elliptic problems
• A discontinuous \(hp\) finite element method for convection-diffusion problems
• Finite element methods and their convergence for elliptic and parabolic interface problems
• New Cartesian grid methods for interface problems using the finite element formulation
• A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow.
• Enriched \(P_1\)-conforming methods for elliptic interface problems with implicit jump conditions
• An IMPES scheme for a two-phase flow in heterogeneous porous media using a structured grid
• The finite element method for elliptic equations with discontinuous coefficients
• A stabilizedP₁-nonconforming immersed finite element method for the interface elasticity problems
• An Analysis of a Broken $P_1$-Nonconforming Finite Element Method for Interface Problems
• Stress analysis around crack tips in finite strain problems using the eXtended finite element method
• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
• New Convergence Estimates for Multigrid Algorithms
• An Optimal-Order Multigrid Method for P1 Nonconforming Finite Elements
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Nonconforming Finite Element Methods for the Equations of Linear Elasticity
• Mixed and Hybrid Finite Element Methods
• The Analysis of Smoothers for Multigrid Algorithms
• On Some Theoretical and Practical Aspects of Multigrid Methods
• Finite volume box schemes on triangular meshes
• Elastic crack growth in finite elements with minimal remeshing
• Structured extended finite element methods for solids defined by implicit surfaces
• Discontinuous Galerkin and the Crouzeix–Raviart element: Application to elasticity
• ConservativeP1 Conforming and Nonconforming Galerkin FEMs: Effective Flux Evaluation via a Nonmixed Method Approach
• A Multigrid Algorithm for the Mortar Finite Element Method
• An immersed finite element space and its approximation capability
• Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems
• Korn's inequalities for piecewise $H^1$ vector fields
• A finite element method for crack growth without remeshing
• Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
• The speed of convergence of one iterative process
• The Analysis of Multigrid Algorithms with Nonnested Spaces or Noninherited Quadratic Forms

This page was built for publication: RECENT DEVELOPMENT OF IMMERSED FEM FOR ELLIPTIC AND ELASTIC INTERFACE PROBLEMS