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Title of Journal: J Sci Comput

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Abbravation: Journal of Scientific Computing

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Kluwer Academic Publishers-Plenum Publishers

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10.1016/0014-4983(80)90009-1

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1573-7691

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Optimal SpectralGalerkin Methods Using Generalize

Authors: BenYu Guo Jie Shen LiLian Wang
Publish Date: 2006/01/10
Volume: 27, Issue: 1-3, Pages: 305-322
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Abstract

We extend the definition of the classical Jacobi polynomials withindexes α β−1 to allow α and/or β to be negative integers We show that the generalized Jacobi polynomials with indexes corresponding to the number of boundary conditions in a given partial differential equation are the natural basis functions for the spectral approximation of this partial differential equation Moreover the use of generalized Jacobi polynomials leads to much simplified analysis more precise error estimates and well conditioned algorithms

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  1. A Hybridized Discontinuous Galerkin Method with Reduced Stabilization
  2. Exact Low-Rank Matrix Completion from Sparsely Corrupted Entries Via Adaptive Outlier Pursuit
  3. Efficient Rearrangement Algorithms for Shape Optimization on Elliptic Eigenvalue Problems
  4. Sparsity Enforcing Edge Detection Method for Blurred and Noisy Fourier data
  5. Semi-Lagrangian Runge-Kutta Exponential Integrators for Convection Dominated Problems
  6. The Finite Volume-Complete Flux Scheme for Advection-Diffusion-Reaction Equations
  7. Simulation of an $$n^{+}\hbox {-}n\hbox {-}n^{+}$$ Diode by Using Globally-Hyperbolically-Closed High-Order Moment Models
  8. Theoretical and Numerical Investigation of the Finite Cell Method
  9. The Effect of the Consistent Mass Matrix on the Maximum-Principle for Scalar Conservation Equations
  10. Analysis of Nonlinear Spectral Eddy-Viscosity Models of Turbulence
  11. Transformation Methods for the Numerical Integration of Three-Dimensional Singular Functions
  12. A Posteriori Estimates for a Natural Neumann–Neumann Domain Decomposition Algorithm on a Unilateral Contact Problem
  13. Solving 1D Conservation Laws Using Pontryagin’s Minimum Principle
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