Immersed finite element method for eigenvalue problem

DOI10.1016/j.cam.2016.09.035zbMath1353.65116arXiv1412.3163OpenAlexW11125969MaRDI QIDQ344296

Imbo Sim, Do Young Kwak, Seung Woo Lee

Publication date: 22 November 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.3163

zbMATH Keywords

stabilityconvergencefinite elementsnumerical experimentelliptic eigenvalue problemimmersed interface

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) 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) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (8)

Eigensolution analysis of immersed boundary method based on volume penalization: applications to high-order schemes ⋮ A meshless Chebyshev collocation method for eigenvalue problems of the Helmholtz equation ⋮ An immersed weak Galerkin method for elliptic interface problems on polygonal meshes ⋮ A nonconforming immersed virtual element method for elliptic interface problems ⋮ A stable RBF partition of unity local method for elliptic interface problems in two dimensions ⋮ A note on the immersed finite element basis functions for elliptic interface problems ⋮ Optimal order error estimates of a modified nonconforming rotated \(Q_1\) IFEM for interface problems ⋮ A generalized isogeometric analysis of elliptic eigenvalue and source problems with an interface

Uses Software

• ARPACK

Cites Work

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• A locking-free immersed finite element method for planar elasticity interface problems
• A posteriori error estimates for non-conforming approximation of eigenvalue problems
• A combined nodal continuous-discontinuous finite element formulation for the Maxwell problem
• 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
• A numerical method for solving variable coefficient elliptic equation with interfaces
• Optimal convergence analysis of an immersed interface finite element method
• A \(p\)-th degree immersed finite element for boundary value problems with discontinuous coefficients
• Approximation of eigenvalues in mixed form, discrete compactness property, and application to \(hp\) mixed finite elements
• Numerical analysis of blood flow in the heart
• The immersed interface method for acoustic wave equations with discontinuous coefficients
• New Cartesian grid methods for interface problems using the finite element formulation
• Perturbation theory for linear operators.
• Convergence analysis of finite element methods for \(H\) (curl; \(\Omega \))-elliptic interface problems
• Discontinuous Galerkin approximation of the Laplace eigenproblem
• An immersed discontinuous finite element method for Stokes interface problems
• Convergence of finite element method for linear second-order wave 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
• The extended/generalized finite element method: An overview of the method and its applications
• IMMERSED BOUNDARY METHODS
• The immersed boundary method
• Estimates for the Errors in Eigenvalue and Eigenvector Approximation by Galerkin Methods, with Particular Attention to the Case of Multiple Eigenvalues
• A Convergent Adaptive Method for Elliptic Eigenvalue Problems
• Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
• Stability of Equilibria for the Stefan Problem With Surface Tension
• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
• Fitted and Unfitted Finite-Element Methods for Elliptic Equations with Smooth Interfaces
• Eigenvalue Approximation by Mixed and Hybrid Methods
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• Spectral Approximation for Compact Operators
• Real Interpolation of Sobolev Spaces on Subdomains of Rn
• On spectral approximation. Part 1. The problem of convergence
• On spectral approximation. Part 2. Error estimates for the Galerkin method
• External finite element approximations of eigenvalue problems
• A Robust Finite Element Method for Nonhomogeneous Dirichlet Problems in Domains with Curved Boundaries
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• ARPACK Users' Guide
• A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems
• On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form
• An immersed finite element space and its approximation capability
• Finite element approximation of spectral problems with Neumann boundary conditions on curved domains
• A finite element method for crack growth without remeshing
• EIGENVALUES OF THE LAPLACIAN ON REGULAR POLYGONS AND POLYGONS RESULTING FROM THEIR DISECTION

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