Solution of 3D-Laplace and Helmholtz equations in exterior domains using \(hp\)-infinite elements
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Publication:1365628
DOI10.1016/0045-7825(95)00987-6zbMath0881.73126OpenAlexW2162386799MaRDI QIDQ1365628
K. Gerdes, Leszek F. Demkowicz
Publication date: 19 February 1998
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(95)00987-6
convergencestability analysisweighted Sobolev spacesvariational formulationexterior spherical domain
Finite element methods applied to problems in solid mechanics (74S05) Wave scattering in solid mechanics (74J20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
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Cites Work
- Unnamed Item
- Unnamed Item
- Solution of elastic scattering problems in linear acoustics using \(h\)-\(p\) boundary element method
- Curved finite element methods for the solution of singular integral equations on surfaces in \(R^3\)
- Asymptotic convergence in finite and boundary element methods. I: Theoretical results
- Asymptotic convergence in finite and boundary element methods. II: The LBB constant for rigid and elastic scattering problems
- Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
- Mapped Wave Envelope Elements for Acoustical Radiation and Scattering
- A Variable Order Infinite Acoustic Wave Envelope Element