Solving interface problems of the Helmholtz equation by immersed finite element methods
DOI10.1007/s42967-019-0002-2zbMath1449.65319OpenAlexW2944369655WikidataQ127900292 ScholiaQ127900292MaRDI QIDQ2289854
Qiao Zhuang, Tao Lin, Yan Ping Lin
Publication date: 27 January 2020
Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s42967-019-0002-2
Helmholtz interface problemshigher degree finite element methodsimmersed finite element (IFE) methods
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) PDEs with low regular coefficients and/or low regular data (35R05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
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- Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient
- A finite element method for interface problems in domains with smooth boundaries and interfaces
- A robust Nitsche's formulation for interface problems
- Composite finite elements for elliptic boundary value problems with discontinuous coefficients
- A priori error estimates for some discontinuous Galerkin immersed finite element methods
- Time harmonic wave diffraction problems in materials with sign-shifting coefficients
- Reflection and transmission of plane waves at an interface between two fluids
- A multiscale finite element method for elliptic problems in composite materials and porous media
- Finite element methods and their convergence for elliptic and parabolic interface problems
- A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime
- New Cartesian grid methods for interface problems using the finite element formulation
- Higher degree immersed finite element spaces constructed according to the actual interface
- Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
- Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
- A phase-based interior penalty discontinuous Galerkin method for the Helmholtz equation with spatially varying wavenumber
- General DG-methods for highly indefinite Helmholtz problems
- The finite element method for elliptic equations with discontinuous coefficients
- Linear continuous interior penalty finite element method for Helmholtz equation With High Wave Number: One-Dimensional Analysis
- Efficient implementation of high‐order finite elements for Helmholtz problems
- The convergence of the bilinear and linear immersed finite element solutions to interface problems
- Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM
- A new multiscale finite element method for high-contrast elliptic interface problems
- A Note on the Numerical Solution of the Wave Equation With Piecewise Smooth Coefficients
- Approximation capability of a bilinear immersed finite element space
- Discontinuous Galerkin Methods for the Helmholtz Equation with Large Wave Number
- Plane wave discontinuous Galerkin methods: Analysis of theh-version
- Fitted and Unfitted Finite-Element Methods for Elliptic Equations with Smooth Interfaces
- Scattering of Electromagnetic Waves by Rough Interfaces and Inhomogeneous Layers
- The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
- APPROXIMATION OF SCALAR WAVES IN THE SPACE-FREQUENCY DOMAIN
- Is the Pollution Effect of the FEM Avoidable for the Helmholtz Equation Considering High Wave Numbers?
- Sommerfeld Diffraction Problems with First and Second Kind Boundary Conditions
- An immersed finite element space and its approximation capability
- Preasymptotic Error Analysis of Higher Order FEM and CIP-FEM for Helmholtz Equation with High Wave Number
- Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
- Nitsche's method for Helmholtz problems with embedded interfaces
- A selective immersed discontinuous Galerkin method for elliptic interface problems
- An Embedded Boundary Method for the Wave Equation with Discontinuous Coefficients
- The Immersed Interface Method
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