A Petrov-Galerkin formulation for the alpha interpolation of FEM and FDM stencils: Applications to the Helmholtz equation

DOI10.1002/nme.3291zbMath1242.65241OpenAlexW1842181531WikidataQ59485464 ScholiaQ59485464MaRDI QIDQ2894960

Prashanth Nadukandi, Eugenio Oñate, Julio García-Espinosa

Publication date: 2 July 2012

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://www.scipedia.com/public/Nadukandi_et_al_2012b

zbMATH Keywords

Helmholtz equationGalerkinPetrovalpha interpolation of FEM and FDMdispersion accuracynonconforming test spaces

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (1)

Revisiting generalized FEM: a Petrov-Galerkin enrichment based FEM interpolation for Helmholtz problem

Cites Work

• Unnamed Item
• The alpha interpolation method for the solution of an eigenvalue problem
• Finite element methods for the Helmholtz equation in an exterior domain: Model problems
• Convergence of the finite element method applied to the eigenvalue problem \(\Delta u+\lambda u=0\)
• Asymptotic convergence in finite and boundary element methods. I: Theoretical results
• Accurate finite difference methods for time-harmonic wave propagation
• High-order finite difference methods for the Helmholtz equation
• A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
• Evaluation of numerical integration methods in elastodynamics
• A fourth-order compact scheme for the Helmholtz equation: Alpha-interpolation of FEM and FDM stencils
• Generalized Difference Methods for a Nonlinear Dirichlet Problem
• Eigenvalues of the Schrödinger Equation by the $\alpha $-Interpolation Method
• Unified Analysis of Finite Volume Methods for Second Order Elliptic Problems
• Arbitrarily Shaped Hollow Waveguide Analysis by the $\alpha $-Interpolation Method
• A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A Galerkin least‐squares finite element method for the two‐dimensional Helmholtz equation
• A quasi optimal Petrov–Galerkin method for Helmholtz problem
• Generalized Functions and Dispersion Relations in Physics

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