Bubble stabilization of Chebyshev-Legendre High-order element methods for the advection-diffusion equation
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The bubble stabilization technique of Chebyshev-Legendre high-order element methods for one dimensional advection-diffusion equation is analyzed for the proposed scheme by Canuto and Puppo in \cite{CP}. We also analyze the finite element lower-order preconditioner for the proposed stabilized linear system. Further, the numerical results are provided to support the developed theories for the convergence and preconditioning.
Abstract
The bubble stabilization technique of Chebyshev-Legendre high-order element methods for one dimensional advection-diffusion equation is analyzed for the proposed scheme by Canuto and Puppo in \cite{CP}. We also analyze the finite element lower-order preconditioner for the proposed stabilized linear system. Further, the numerical results are provided to support the developed theories for the convergence and preconditioning.
참고문헌 (13)
- C. Baiocchi, "Virtual bubbles and Galerkin-least-squares type methods", Comput. Methods Appl. Mech. Engrg, 105(1), pp.125~142 (1993)
- F. Brezzi, "A relationship be-tween stabilized finite element methods and the Galerkin Method with bubble functions", Comput. Methods Appl. Mech. Engrg, 96(1), pp.117~130 (1992)
- A. N. T. Brooks, "Streamline upwind", Petrov-Galerkin formulations for convected dominated flows with a particular emphasis on the incompressible Navier-Stokes equations, 1982, pp.32(1-3), 199~259
- C. Canuto, "Spectral methods and a maximum principle", Math. Comp, 51(184), pp.615~629 (1988)
- C. Canuto, "Stabilization of spectral methods by finite element bubble functions", Comput. Methods Appl. Mech. Engrg, 116(1-4), pp.13~26 (1994)
- C. Canuto, "Spectral Methods. Funda-mentals in Single Domains" (2006), Springer-Verlag
- C. Canuto, "Spectral Methods. Evolution to Complex Geometries and Applications to Flid Dynamics" (2007), Springer-Verlag
- C. Canuto, "Bubble stabilization of spectral Legendre methods for the advection-diffusion equation", Comput. Methods Appl. Mech. Engrg, 118(3-4), pp.239~263 (1994)
- S. D. Kim, "Piecewise bilinear preconditioning of high-order finite element methods", Elec-tron. Trans. Numer. Anal, 26, pp.228~242 (2007)
- S. Kim, "Preconditioning on high-order element methods using Chebyshev-Gauss-Lobatto nodes", Appl. Numer. Math, 59, pp.316~333 (2009)
- S. D. Kim, "Preconditioning Chebyshev spectral collocation method for elliptic partial differential equations", SIAM J. Numer. Anal, 33(6), pp.2375~2400 (1996)
- J. H. Lee, "Bubble Stabilization of Chebyshev Spectral Method for Advection-Diffusion Equation", Ph.D., pp.1988
- H. Ma, "Chebyshev-Legendre spectral viscosity method for nonlinear conservation laws", SIAM J. Numer. Anal, 35(3), pp.869~892 (1998)