DOI10.1137/S0036142995285873zbMath0955.65081OpenAlexW1967469744MaRDI QIDQ4389124
Bruno Després, Olivier Cessenat
Publication date: 11 May 1998
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/s0036142995285873
Viscous Equations Treated with $$\mathcal{L}$$ -Splines and Steklov-Poincaré Operator in Two Dimensions ⋮
Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions ⋮
Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons ⋮
On Stability of Discretizations of the Helmholtz Equation ⋮
Adaptive refinement for \(hp\)-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem ⋮
A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation ⋮
Error estimates in the fast multipole method for scattering problems Part 1: Truncation of the Jacobi-Anger series ⋮
A Posteriori Error Estimation of $hp$-$dG$ Finite Element Methods for Highly Indefinite Helmholtz Problems ⋮
A space-time discontinuous Galerkin method for linear hyperbolic PDE's with high frequencies ⋮
Unnamed Item ⋮
A hybridizable discontinuous Galerkin method with characteristic variables for Helmholtz problems ⋮
A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation ⋮
A partition of unity FEM for time-dependent diffusion problems using multiple enrichment functions ⋮
Improvements for the ultra weak variational formulation ⋮
Efficiency of high-order elements for continuous and discontinuous Galerkin methods ⋮
A comparison of techniques for overcoming non-uniqueness of boundary integral equations for the collocation partition of unity method in two-dimensional acoustic scattering ⋮
Analysis of high-order finite elements for convected wave propagation ⋮
Dispersion analysis of plane wave discontinuous Galerkin methods ⋮
Efficient DG-like formulation equipped with curved boundary edges for solving elasto-acoustic scattering problems ⋮
Mixed enrichment for the finite element method in heterogeneous media ⋮
A discontinuous Galerkin method with plane waves for sound-absorbing materials ⋮
Novel Multilevel Preconditioners for the Systems Arising from Plane Wave Discretization of Helmholtz Equations with Large Wave Numbers ⋮
Efficient implementation of high‐order finite elements for Helmholtz problems ⋮
A quasi-optimal coarse problem and an augmented Krylov solver for the variational theory of complex rays ⋮
A Trefftz method with reconstruction of the normal derivative applied to elliptic equations ⋮
A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation ⋮
Embedded Trefftz discontinuous Galerkin methods ⋮
NonLocal Optimized Schwarz Method for the Helmholtz Equation with Physical Boundaries ⋮
Wavenumber Explicit Convergence of a Multiscale Generalized Finite Element Method for Heterogeneous Helmholtz Problems ⋮
Ultra-weak variational formulation for heterogeneous Maxwell problem in the context of high performance computing ⋮
At the interface between semiclassical analysis and numerical analysis of wave scattering problems. Abstracts from the workshop held September 25 -- October 1, 2022 ⋮
Frequency domain Bernstein-Bézier finite element solver for modelling short waves in elastodynamics ⋮
A superconvergent ultra-weak discontinuous Galerkin method for nonlinear second-order two-point boundary-value problems ⋮
Stable approximation of Helmholtz solutions in the disk by evanescent plane waves ⋮
A Novel Deep Neural Network Algorithm for the Helmholtz Scattering Problem In the Unbounded Domain ⋮
A unified theory of non-overlapping Robin-Schwarz methods: continuous and discrete, including cross points ⋮
Stability of systems governed by elliptic partial differential equations ⋮
A Survey of Trefftz Methods for the Helmholtz Equation ⋮
Variational Multiscale Stabilization and the Exponential Decay of Fine-Scale Correctors ⋮
Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems ⋮
THE VARIATIONAL THEORY OF COMPLEX RAYS FOR THREE-DIMENSIONAL HELMHOLTZ PROBLEMS ⋮
Hybrid Finite Element Method and Variational Theory of Complex Rays for Helmholtz Problems ⋮
Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation ⋮
A Novel Least Squares Method for Helmholtz Equations with Large Wave Numbers ⋮
Robust Adaptive $hp$ Discontinuous Galerkin Finite Element Methods for the Helmholtz Equation ⋮
A space-time discontinuous Galerkin method for the solution of the wave equation in the time domain ⋮
Three-dimensional element configurations for the discontinuous enrichment method for acoustics ⋮
An Overview of the Discontinuous Petrov Galerkin Method ⋮
The Trefftz method for the Helmholtz equation with degeneracy ⋮
The Plane Wave Methods Combined with Local Spectral Finite Elements for the Wave Propagation in Anisotropic Media ⋮
THE MULTISCALE VTCR APPROACH APPLIED TO ACOUSTICS PROBLEMS ⋮
An ultra-weak method for acoustic fluid-solid interaction ⋮
The Plane Wave Methods for the Time-Harmonic Elastic Wave Problems with the Complex Valued Coefficients ⋮
Fast Computation of High‐Frequency Dirichlet Eigenmodes via Spectral Flow of the Interior Neumann‐to‐Dirichlet Map ⋮
Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations ⋮
A comparison of wave-based discontinuous Galerkin, ultra-weak and least-square methods for wave problems ⋮
Error Analysis of the Plane Wave Discontinuous Galerkin Method for Maxwell’s Equations in Anisotropic Media ⋮
A mixed hybrid finite element method for the Helmholtz equation ⋮
AN ADAPTIVE NUMERICAL STRATEGY FOR THE MEDIUM-FREQUENCY ANALYSIS OF HELMHOLTZ'S PROBLEM ⋮
A least-squares finite element method for solving the polygonal-line arc-scattering problem ⋮
Substructuring Preconditioners for the Systems Arising from Plane Wave Discretization of Helmholtz Equations ⋮
Plane wave decomposition in the unit disc: convergence estimates and computational aspects ⋮
Calculation of medium-frequency vibrations over a wide frequency range ⋮
A STUDY OF HIGHER-ORDER DISCONTINUOUS GALERKIN AND QUADRATIC LEAST-SQUARES STABILIZED FINITE ELEMENT COMPUTATIONS FOR ACOUSTICS ⋮
Unnamed Item ⋮
Comparison of two wave element methods for the Helmholtz problem ⋮
A discontinuous enrichment method for the efficient solution of plate vibration problems in the medium-frequency regime ⋮
The extended/generalized finite element method: An overview of the method and its applications ⋮
Improvement of PUFEM for the numerical solution of high-frequency elastic wave scattering on unstructured triangular mesh grids ⋮
Adaptive numerical solution of a discontinuous Galerkin method for a Helmholtz problem in low-frequency regime ⋮
Exact integration of polynomial-exponential products with application to wave-based numerical methods ⋮
Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method ⋮
Discontinuous Galerkin methods with Trefftz approximations ⋮
Implementation of an interior point source in the ultra weak variational formulation through source extraction ⋮
Plane wave discontinuous Galerkin methods: Analysis of theh-version ⋮
A plane wave virtual element method for the Helmholtz problem ⋮
A Primal-Dual Weak Galerkin Finite Element Method for Fokker--Planck Type Equations ⋮
A nonconforming Trefftz virtual element method for the Helmholtz problem ⋮
A variant of the plane wave least squares method for the time-harmonic Maxwell’s equations ⋮
A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers ⋮
Amplitude-based Generalized Plane Waves: New Quasi-Trefftz Functions for Scalar Equations in two dimensions ⋮
Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures ⋮
Feedforward and feedback control of ultrasound surgery ⋮
Residual-Based Adaptivity and PWDG Methods for the Helmholtz Equation ⋮
Nitsche's method for Helmholtz problems with embedded interfaces ⋮
Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers ⋮
A fourth-order compact scheme for the Helmholtz equation: Alpha-interpolation of FEM and FDM stencils ⋮
Dispersion error reduction for acoustic problems using the edge-based smoothed finite element method (ES-FEM) ⋮
3D mass-redistributed finite element method in structural-acoustic interaction problems ⋮
Wave boundary elements: a theoretical overview presenting applications in scattering of short waves ⋮
Preasymptotic error analysis of the HDG method for Helmholtz equation with large wave number ⋮
An edge multiscale interior penalty discontinuous Galerkin method for heterogeneous Helmholtz problems with large varying wavenumber ⋮
Local strategies for improving the conditioning of the plane-wave ultra-weak variational formulation ⋮
Nonstandard finite element methods. Abstracts from the workshop held January 10--16, 2021 (hybrid meeting) ⋮
Numerical microlocal analysis of harmonic wavefields ⋮
Numerical modeling of undersea acoustics using a partition of unity method with plane waves enrichment ⋮
A survey of finite element methods for time-harmonic acoustics ⋮
Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version ⋮
Well-posedness and generalized plane waves simulations of a 2D mode conversion model ⋮
High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments ⋮
Trefftz-based methods for time-harmonic acoustics ⋮
A first order system least squares method for the Helmholtz equation ⋮
Discontinuous Galerkin methods with plane waves for time-harmonic problems ⋮
A discontinuous finite element formulation for Helmholtz equation ⋮
A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes ⋮
Solving a scattering problem in near field optics by a least-squares method ⋮
The ultra weak variational formulation of thin clamped plate problems ⋮
A phase-based hybridizable discontinuous Galerkin method for the numerical solution of the Helmholtz equation ⋮
Extended variational theory of complex rays in heterogeneous Helmholtz problem ⋮
A DPG method for shallow shells ⋮
A plane wave discontinuous Galerkin method with a Dirichlet-to-Neumann boundary condition for the scattering problem in acoustics ⋮
A local wave tracking strategy for efficiently solving mid- and high-frequency Helmholtz problems ⋮
On Trefftz and weak Trefftz discontinuous Galerkin approaches for medium-frequency acoustics ⋮
Trefftz discontinuous Galerkin basis functions for a class of Friedrichs systems coming from linear transport ⋮
DPG method with optimal test functions for a fractional advection diffusion equation ⋮
A mixed hybrid formulation based on oscillated finite element polynomials for solving Helmholtz problems ⋮
A compact fourth order scheme for the Helmholtz equation in polar coordinates ⋮
A meshless numerical method for time harmonic quasi-periodic scattering problem ⋮
An ultra-weak discontinuous Galerkin method for Schrödinger equation in one dimension ⋮
The numerical solution of the acoustic wave scattering from penetrable obstacles by a least-squares method ⋮
A symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation ⋮
Vekua theory for the Helmholtz operator ⋮
Plane wave approximation of homogeneous Helmholtz solutions ⋮
A mass-redistributed finite element method (MR-FEM) for acoustic problems using triangular mesh ⋮
A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime ⋮
Interpolation properties of generalized plane waves ⋮
Adaptive-multilevel BDDC algorithm for three-dimensional plane wave Helmholtz systems ⋮
A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations ⋮
An efficient wave based method for solving Helmholtz problems in three-dimensional bounded domains ⋮
Variational theory of complex rays applied to shell structures: in-plane inertia, quasi-symmetric ray distribution, and orthotropic materials ⋮
Asymptotically derived boundary elements for the Helmholtz equation in high frequencies ⋮
Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation ⋮
Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension ⋮
General DG-methods for highly indefinite Helmholtz problems ⋮
The discontinuous enrichment method for multiscale analysis. ⋮
A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations ⋮
Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes ⋮
A comparison of high-order and plane wave enriched boundary element basis functions for Helmholtz problems ⋮
A least-squares method for the Helmholtz equation ⋮
Modeling aspects to improve the solution of the inverse problem in scatterometry ⋮
On some results about the variational theory of complex rays used close to the high frequency regime ⋮
An improved cell-based smoothed radial point interpolation method using condensed shape functions for 3D interior acoustic problems ⋮
Iterative solution applied to the Helmholtz equation: complex deflation on unstructured grids ⋮
An efficient Wave Based Method for 2D acoustic problems containing corner singularities ⋮
Bernstein-Bézier based finite elements for efficient solution of short wave problems ⋮
A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects ⋮
Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number ⋮
Trefftz discontinuous Galerkin method for Friedrichs systems with linear relaxation: application to the \(P_1\) model ⋮
A numerical algorithm to reduce ill-conditioning in meshless methods for the Helmholtz equation ⋮
A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation ⋮
\(\mathcal L\)-splines and viscosity limits for well-balanced schemes acting on linear parabolic equations ⋮
Discontinuous Petrov-Galerkin boundary elements ⋮
On the use of the variational theory of complex rays for the analysis of 2-D exterior Helmholtz problem in an unbounded domain ⋮
FEM with Trefftz trial functions on polyhedral elements ⋮
The Fourier version of the variational theory of complex rays for medium-frequency acoustics ⋮
DPG method with optimal test functions for a transmission problem ⋮
Wavelet based ILU preconditioners for the numerical solution by PUFEM of high frequency elastic wave scattering ⋮
Numerical evaluation of the two-dimensional partition of unity boundary integrals for Helmholtz problems ⋮
A comparison of NRBCs for PUFEM in 2D Helmholtz problems at high wave numbers ⋮
An unconditionally stable discontinuous Galerkin method for the elastic Helmholtz equations with large frequency ⋮
Wave interpolation finite elements for Helmholtz problems with jumps in the wave speed ⋮
A plane wave least squares method for the Maxwell equations in anisotropic media ⋮
Smoothed finite element methods (S-FEM): an overview and recent developments ⋮
Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers ⋮
A comparison of high-order polynomial and wave-based methods for Helmholtz problems ⋮
The method of polarized traces for the 2D Helmholtz equation ⋮
Superconvergence of ultra-weak discontinuous Galerkin methods for the linear Schrödinger equation in one dimension ⋮
Implementation and computational aspects of a 3D elastic wave modelling by PUFEM ⋮
The ultra weak variational formulation for the modified mild-slope equation ⋮
Higher order finite and infinite elements for the solution of Helmholtz problems ⋮
The discontinuous enrichment method for medium-frequency Helmholtz problems with a spatially variable wavenumber ⋮
Plane wave discontinuous Galerkin methods for the Helmholtz equation and Maxwell equations in anisotropic media ⋮
Model reduction in state identification problems with an application to determination of thermal parameters ⋮
Effect of enrichment functions on GFEM solutions of time-dependent conduction heat transfer problems ⋮
A combined scheme of the local spectral element method and the generalized plane wave discontinuous Galerkin method for the anisotropic Helmholtz equation ⋮
An ultra-weak discontinuous Galerkin method with implicit-explicit time-marching for generalized stochastic KdV equations ⋮
Higher-order meshing of implicit geometries. I: Integration and interpolation in cut elements ⋮
Exact integration scheme for planewave-enriched partition of unity finite element method to solve the Helmholtz problem ⋮
A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber ⋮
On wave based weak Trefftz discontinuous Galerkin approach for medium-frequency heterogeneous Helmholtz problem ⋮
Plane wave enriched partition of unity isogeometric analysis (PUIGA) for 2D-Helmholtz problems ⋮
Analysis of the numerical dispersion of waves in saturated poroelastic media ⋮
Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations ⋮
A partition of unity finite element method for nonlinear transient diffusion problems in heterogeneous materials ⋮
A Trefftz-discontinuous Galerkin method for time-harmonic elastic wave problems ⋮
An oversampled collocation approach of the wave based method for Helmholtz problems ⋮
The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation ⋮
Computational aspects of the ultra-weak variational formulation