Topic
Spectral element method
About: Spectral element method is a research topic. Over the lifetime, 3250 publications have been published within this topic receiving 111107 citations.
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Papers
Book•
26 Jun 1995
TL;DR: The Finite Element Method as mentioned in this paper is a method for linear analysis in solid and structural mechanics, and it has been used in many applications, such as heat transfer, field problems, and Incompressible Fluid Flows.
Abstract: 1. An Introduction to the Use of Finite Element Procedures. 2. Vectors, Matrices and Tensors. 3. Some Basic Concepts of Engineering Analysis and an Introduction to the Finite Element Methods. 4. Formulation of the Finite Element Method -- Linear Analysis in Solid and Structural Mechanics. 5. Formulation and Calculation of Isoparametric Finite Element Matrices. 6. Finite Element Nonlinear Analysis in Solid and Structural Mechanics. 7. Finite Element Analysis of Heat Transfer, Field Problems, and Incompressible Fluid Flows. 8. Solution of Equilibrium Equations in State Analysis. 9. Solution of Equilibrium Equations in Dynamic Analysis. 10. Preliminaries to the Solution of Eigenproblems. 11. Solution Methods for Eigenproblems. 12. Implementation of the Finite Element Method. References. Index.
11,399 citations
Book•
1 Feb 1987
4,927 citations
1 Jan 1977
TL;DR: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of algebraic stability analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Method as discussed by the authors.
Abstract: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of Algebraic Stability Analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Methods Numerical Results for Hyperbolic Problems Advection-Diffusion Equation Models of Incompressible Fluid Dynamics Miscellaneous Applications of Spectral Methods Survey of Spectral Methods and Applications Properties of Chebyshev and Legendre Polynomial Expansions.
3,797 citations
3,121 citations
TL;DR: In this article, a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved, which can therefore be more efficient than the usual finite element methods.
Abstract: A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved This new method can therefore be more efficient than the usual finite element methods An additional feature of the partition-of-unity method is that finite element spaces of any desired regularity can be constructed very easily This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers The basic estimates for a posteriori error estimation for this new method are also proved © 1997 by John Wiley & Sons, Ltd
2,568 citations
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| Year | Papers |
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| 2025 | 10 |
| 2024 | 16 |
| 2023 | 26 |
| 2022 | 58 |
| 2021 | 87 |
| 2020 | 79 |