Wavenumber-explicit stability and convergence analysis of ℎ𝑝 finite element discretizations of Helmholtz problems in piecewise smooth media

Maximilian Bernkopf, T. Chaumont-Frelet, Jens Markus Melenk

Type: Article

Publication Date: 2024-03-29

Citations: 2

DOI: https://doi.org/10.1090/mcom/3958

View Publication

Locations

Mathematics of Computation - View
arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Wavenumber-explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers	2021	Théophile Chaumont-Frelet Dietmar Gallistl Serge Nicaise Jérôme Tomezyk
+	Wavenumber-explicit convergence of the $hp$-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients	2020	David Lafontaine Euan A. Spence Jared Wunsch
+	Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients	2022	D. Lafontaine Euan A. Spence Jared Wunsch
+	Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations	2021	Yifan Chen Thomas Y. Hou Yixuan Wang
+	Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations.	2021	Yifan Chen Thomas Y. Hou Yixuan Wang
+	The $hp$-FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect	2022	Jeffrey Galkowski David Lafontaine Euan A. Spence Jared Wunsch
+	Solvability of Discrete Helmholtz Equations	2021	Maximilian Bernkopf Stefan Sauter Céline Torres Alexander Veit
+	Stability analysis of heterogeneous Helmholtz problems and finite element solution based on propagation media approximation	2016	Hélène Barucq Théophile Chaumont-Frelet Christian Gout
+	Robust adaptive hp discontinuous Galerkin finite element methods for the Helmholtz equation	2018	Scott Congreve Joscha Gedicke Ilaria Perugia
+	Robust adaptive hp discontinuous Galerkin finite element methods for the Helmholtz equation	2018	Scott Congreve Joscha Gedicke Ilaria Perugia
+ PDF Chat	Wavenumber Explicit Convergence of a Multiscale Generalized Finite Element Method for Heterogeneous Helmholtz Problems	2023	Chupeng Ma Christian Alber Robert Scheichl
+ PDF Chat	Robust Adaptive $hp$ Discontinuous Galerkin Finite Element Methods for the Helmholtz Equation	2019	Scott Congreve Joscha Gedicke Ilaria Perugia
+	Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions	2022	Jens Markus Melenk Stefan Sauter
+	Analysis of the $hp$-version of a first order system least squares method for the Helmholtz equation	2018	Maximilian Bernkopf Jens Markus Melenk
+	Numerical methods for Helmholtz-type equations in unbounded regions	2008	Charles I. Goldstein
+ PDF Chat	Wavenumber Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems	2020	Jens Markus Melenk Stefan Sauter Céline Torres
+ PDF Chat	On Edge Multiscale Space based Hybrid Schwarz Preconditioner for Helmholtz Problems with Large Wavenumbers	2024	Shubin Fu Shihua Gong Guanglian Li Xu Wang
+	A hybrid approach to solve the high-frequency Helmholtz equation with source singularity	2017	Jun Fang Jianliang Qian Leonardo Zepeda-Núñez Hongkai Zhao
+	Analysis of the $hp$-version of a first order system least squares method for the Helmholtz equation.	2018	Maximilian Bernkopf Jens Markus Melenk
+	Wavenumber explicit convergence of a multiscale generalized finite element method for heterogeneous Helmholtz problems	2021	Chupeng Ma Christian Alber Robert Scheichl

Works That Cite This (2)

Action	Title	Year	Authors
+	Wavenumber-explicit stability and convergence analysis of ℎ𝑝 finite element discretizations of Helmholtz problems in piecewise smooth media	2024	Maximilian Bernkopf T. Chaumont-Frelet Jens Markus Melenk
+ PDF Chat	At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems	2023	Simon N. Chandler‐Wilde Monique Dauge Euan A. Spence Jared Wunsch

Works Cited by This (33)

Action	Title	Year	Authors
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+ PDF Chat	Sharp High-Frequency Estimates for the Helmholtz Equation and Applications to Boundary Integral Equations	2016	Dean Baskin Euan A. Spence Jared Wunsch
+ PDF Chat	The Perfectly Matched Layer in Curvilinear Coordinates	1998	Francis Collino Peter Monk
+ PDF Chat	Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: $hp$ Version	2013	Lingxue Zhu Haijun Wu
+	Analysis of a coupled finite-infinite element method for exterior Helmholtz problems	2001	Leszek Demkowicz Frank Ihlenburg
+ PDF Chat	Wavenumber-Explicit Bounds in Time-Harmonic Acoustic Scattering	2014	Euan A. Spence
+	A direct boundary integral equation method for transmission problems	1985	Martin Costabel Ernst P. Stephan
+ PDF Chat	Decay of solutions of the wave equation in the exterior of several convex bodies	1988	Mitsuru Ikawa
+	ON THE SHORT WAVE ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF STATIONARY PROBLEMS AND THE ASYMPTOTIC BEHAVIOUR AS<i>t</i>→ ∞ OF SOLUTIONS OF NON-STATIONARY PROBLEMS	1975	B. Vaĭnberg
+ PDF Chat	Mapping Properties of Combined Field Helmholtz Boundary Integral Operators	2012	Jens Markus Melenk