A least-squares finite element method for the Helmholtz equation

DOI10.1016/0045-7825(90)90121-2zbMath0726.65121OpenAlexW2078369659MaRDI QIDQ804263

Ching-Lung Chang

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0045-7825(90)90121-2

zbMATH Keywords

convergencenumerical exampleSobolev spaceerror estimatesfinite element methodHelmholtz equationfirst order system

Mathematics Subject Classification ID

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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

A first order system least squares method for the Helmholtz equation, On the use of physical spline finite element method for acoustic scattering, Quasi-least-squares finite element method for steady flow and heat transfer with system rotation, A new scheme to obtain pollution-free solution for plane waves and to generate a continuous Petrov-Galerkin method for the Helmholtz problem, Discontinuous Galerkin method for the Helmholtz transmission problem in two-level homogeneous media, A discontinuous least squares finite element method for the Helmholtz equation, Application of He's homotopy perturbation method for multi‐dimensional fractional Helmholtz equation, Parallel least-squares finite element method for time-dependent convection-diffusion system, Staggered discontinuous Galerkin methods for the Helmholtz equation with large wave number, Some least-squares Galerkin procedures for first-order time-dependent convection-diffusion system, Solution of Helmholtz equation by differential quadrature method, Unnamed Item, A split least-squares characteristic mixed element method for nonlinear nonstationary convection–diffusion problem, The Trefftz method for the Helmholtz equation with degeneracy, Error estimates and adaptive finite element methods, Pre-asymptotic error analysis of \(hp\)-interior penalty discontinuous Galerkin methods for the Helmholtz equation with large wave number, Analysis of least-squares mixed finite element methods for nonlinear nonstationary convection-diffusion problems, Error estimates for least-squares mixed finite elements, Improved discretization error estimates for first-order system least squares, ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number, Object-oriented programming of adaptive finite element and finite volume methods, A unified analysis of a weighted least squares method for first-order systems, Least-square finite element method for electromagnetic fields in 2-D, An analysis of the eddy current problem by the least-squares finite element in 2-D

Cites Work

• Unnamed Item
• Unnamed Item
• On different finite element methods for approximating the gradient of the solution to the Helmholtz equation
• A finite element method for first order elliptic systems in three dimensions
• On finite element methods of the least squares type
• Interior estimates for elliptic systems of partial differential equations
• On the Numerical Solutions of Helmholtz’s Equation by the Finite Element Method
• CONJUGATE PROBLEMS OF ELLIPTIC DIFFERENTIAL AND PSEUDODIFFERENTIAL BOUNDARY VALUE PROBLEMS IN A BOUNDED DOMAIN
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
• A Subdomain–Galerkin/Least Squares Method for First-Order Elliptic Systems in the Plane