Fully discrete \(hp\)-finite elements: Fast quadrature
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Publication:5939409
DOI10.1016/S0045-7825(00)00322-4zbMath0985.65141OpenAlexW1980005758MaRDI QIDQ5939409
K. Gerdes, Christoph Schwab, Jens Markus Melenk
Publication date: 27 May 2002
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0045-7825(00)00322-4
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Uses Software
Cites Work
- Unnamed Item
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- Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure
- A spectral element method for fluid dynamics: Laminar flow in a channel expansion
- Spectral methods for problems in complex geometries
- Spectral approximation for elliptic boundary value problems
- HP90: A general and flexible Fortran 90 \(hp\)-FE code
- Non-overlapping domain decomposition methods for adaptive \(hp\) approximations of the Stokes problem with discontinuous pressure fields
- A spectral element methodology tuned to parallel implementations
- Hierarchic models for laminated plates and shells
- Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems
- Finite Element Preconditioning for Legendre Spectral Collocation Approximations to Elliptic Equations and Systems
- Thepandh-pVersions of the Finite Element Method, Basic Principles and Properties
- Parallel Domain Decomposition Solver for Adaptive hp Finite Element Methods
- An Additive Schwarz Method for the h-p Version of the Finite Element Method in Three Dimensions
- A Polylogarithmic Bound for an Iterative Substructuring Method for Spectral Elements in Three Dimensions
- A Preconditioner Based on Domain Decomposition forh-pFinite-Element Approximation on Quasi-Uniform Meshes
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