Bull. Korean Math. Soc. 2016; 53(2): 423-440
Printed March 31, 2016
https://doi.org/10.4134/BKMS.2016.53.2.423
Copyright © The Korean Mathematical Society.
Philsu Kim, Sang Dong Kim, and Yong Hun Lee
Kyungpook National University, University of Wisconsin-Whitewater, Chonbuk National University
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.
Keywords: Chebyshev-Galerkin spectral method, bubble-stabilization, advection-diffusion equation, lower-order preconditioner
MSC numbers: Primary 65L60, 65L20, 65F08
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