A nearly optimal Galerkin projected residual finite element method for Helmholtz problem

DOI10.1016/j.cma.2007.11.001zbMath1159.65357OpenAlexW2058626175MaRDI QIDQ1013911

Abimael Fernando Dourado Loula, Gustavo Benitez Alvarez, Eduardo Gomes Dutra Do Carmo, Fernando Alves Rochinha

Publication date: 23 April 2009

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

Full work available at URL: http://hdl.handle.net/11422/8812

zbMATH Keywords

finite element methodstabilizationHelmholtz equationGLSGGLSGPR

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Hydro- and aero-acoustics (76Q05) Finite element methods applied to problems in fluid mechanics (76M10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

Galerkin projected residual method applied to diffusion-reaction problems, A quasi optimal Petrov–Galerkin method for Helmholtz problem, A symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation, Quasi optimal finite difference method for Helmholtz problem on unstructured grids, The size function for a HDG method applied to the Helmholtz problem, A fourth-order compact scheme for the Helmholtz equation: Alpha-interpolation of FEM and FDM stencils

Cites Work

• Unnamed Item
• Unnamed Item
• The Galerkin gradient least-squares method
• Finite element methods for the Helmholtz equation in an exterior domain: Model problems
• Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains
• Finite element analysis of acoustic scattering
• A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime
• The nearly-optimal Petrov-Galerkin method for convection-diffusion problems.
• Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
• A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
• A discontinuous finite element formulation for Helmholtz equation
• The generalized finite element method for Helmholtz equation: theory, computation, and open problems
• A discontinuous finite element method at element level for Helmholtz equation
• Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods
• Galerkin projected residual method applied to diffusion-reaction problems
• Bubble-based stabilization for the Helmholtz equation
• Residual-free bubbles for the Helmholtz equation
• A Galerkin least‐squares finite element method for the two‐dimensional Helmholtz equation
• A locally discontinuous enriched finite element formulation for acoustics
• Nearly \(H^1\)-optimal finite element methods