Legendre and Chebyshev dual-Petrov-Galerkin methods for hyperbolic equations
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Publication:1033395
DOI10.1016/j.cma.2006.10.031zbMath1173.65342OpenAlexW2041588624MaRDI QIDQ1033395
Publication date: 6 November 2009
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2006.10.031
Chebyshev polynomialshyperbolic problemsLegendre polynomialsdual-Petrov-Galerkin methodspectral and pseudo-spectral approximations
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Initial-boundary value problems for first-order hyperbolic systems (35L50)
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Cites Work
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- Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
- Spectral methods for problems in complex geometries
- On the stability of the unsmoothed Fourier method for hyperbolic equations
- Stability of Gauss-Radau pseudospectral approximations of the one-dimensional wave equation
- Preconditioned minimal residual methods for Chebyshev spectral calculations
- Optimal estimates for lower and upper bounds of approximation errors in the \(p\)-version of the finite element method in two dimensions
- On the dual Petrov-Galerkin formulation of the KdV equation on a finite interval
- Optimal spectral-Galerkin methods using generalized Jacobi polynomials
- Preconditioning Legendre Spectral Collocation Methods for Elliptic Problems II: Finite Element Operators
- The CFL Condition for Spectral Approximations to Hyperbolic Initial-Boundary Value Problems
- The Stability of Pseudospectral-Chebyshev Methods
- Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
- Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials
- A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KDV Equation
- Error Estimates for Spectral and Pseudospectral Approximations of Hyperbolic Equations
- Spectral methods for hyperbolic problems
