Stable Spectral Methods with No Spurious EigenvaluesUniversity of Wisconsin--Madison, 2005 - 167 pages |
Common terms and phrases
2nd kind 3rd kind a₁ Approximation error Bessel polynomials calculations chapter characteristic polynomial Chebyshev Galerkin method Chebyshev polynomials Chebyshev-Tau method CN+1 coefficients compute corresponding Dēk differentiation implementation eigenproblem eigenvalue problem equal to zero equivalent expansion functions following differential equation fourth order problem Galerkin method Gegenbauer polynomials Gegenbauer-Galerkin method Gegenbauer-Inviscid Galerkin method Gegenbauer-Tau method given Gottlieb and Orszag heat equation Inviscid Inviscid-Galerkin Jacobi polynomials Legendre polynomials lemma Lundblahd matrix model problem Navier-Stokes equations no-slip boundary conditions Orr-Sommerfeld orthogonal polynomials Phi formulation Pn(x polynomial approximation polynomial of degree polynomial solution positive pair problem 2.5 proof real and negative right hand side roundoff errors satisfies the following second derivative solve spectral methods spurious eigenvalues stable polynomials Stokes equations T₁ T₂ terms of Chebyshev test functions theorem three methods Waleffe Weighted Residuals Σ μ