An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations

DOI10.1016/j.cma.2010.08.003zbMath1225.74078OpenAlexW2046048396MaRDI QIDQ643946

M. Scheble, María Gabriela Armentano, Claudio Padra, Rodolfo Rodríguez

Publication date: 2 November 2011

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2010.08.003

zbMATH Keywords

finite elements\(hp\) versionfluidA posteriori error estimatesspectral approximationstructure interactionvibration problem

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Finite element methods applied to problems in solid mechanics (74S05)

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Cites Work

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• Toward a universal h-p adaptive finite element strategy. II: A posteriori error estimation
• A new \(hp\) method for the \(-\mathrm{grad}(\mathrm{div})\) operator in non-Cartesian geometries
• The application of the \(hp\)-finite element method to electromagnetic problems
• Approximation of eigenvalues in mixed form, discrete compactness property, and application to \(hp\) mixed finite elements
• A two-dimensional self-adaptive \(hp\) finite element method for the characterization of waveguide discontinuities. II: Goal-oriented \(hp\)-adaptivity
• A two-dimensional self-adaptivehpfinite element method for the characterization of waveguide discontinuities. I: Energy-norm based automatichp-adaptivity
• The h-p version of the finite element method. I. The basic approximation results
• The h-p version of the finite element method. II. General results and applications
• Eigenfrequencies of a tube bundle placed in a confined fluid
• Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers
• Approximation properties of the \(h\)-\(p\) version of the finite element method
• An adaptive refinement strategy for \(hp\)-finite element computations
• A finite element solution of an added mass formulation for coupled fluid-solid vibrations
• Evidence of exponential convergence in the computation of Maxwell eigenvalues
• Natural frequencies of tube bundle in an incompressible fluid
• A posteriori error estimates for the Steklov eigenvalue problem
• A Posteriori Error Estimates for the Finite Element Approximation of Eigenvalue Problems
• Computation of resonant modes for axisymmetric Maxwell cavities usinghp-version edge finite elements
• Discrete Compactness for the hp Version of Rectangular Edge Finite Elements
• The $h-p$ version of the finite element method with quasiuniform meshes
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries
• Regularity and Numerical Solution of Eigenvalue Problems with Piecewise Analytic Data
• Asymptotic Analysis Relating Spectral Models in Fluid--Solid Vibrations
• A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems
• A POSTERIORI ERROR ESTIMATORS FOR MIXED APPROXIMATIONS OF EIGENVALUE PROBLEMS
• Computing with hp-ADAPTIVE FINITE ELEMENTS
• The effect of reduced integration in the Steklov eigenvalue problem
• Computing with hp-ADAPTIVE FINITE ELEMENTS
• A posteriori estimates for the Stokes eigenvalue problem
• Ana posteriorierror estimator for thep- andhp-versions of the finite element method
• On residual-based a posteriori error estimation in hp-FEM