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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.

Bubble stabilization of Chebyshev-Legendre High-order element methods for the advection-diffusion equation

Philsu Kim, Sang Dong Kim, and Yong Hun Lee

Kyungpook National University, University of Wisconsin-Whitewater, Chonbuk National University

Abstract

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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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