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ANALYSIS OF A LOCAL DISCONTINUOUS GALERKIN METHOD FOR LINEAR TIME-DEPENDENT FOURTH-ORDER PROBLEMS

BO DONG and CHI-WANG SHU
SIAM Journal on Numerical Analysis
Vol. 47, No. 5 (2009), pp. 3240-3268
Stable URL: http://www.jstor.org/stable/25735312
Page Count: 29
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ANALYSIS OF A LOCAL DISCONTINUOUS GALERKIN METHOD FOR LINEAR TIME-DEPENDENT FOURTH-ORDER PROBLEMS
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Abstract

We analyze a local discontinuous Galerkin method for fourth-order time-dependent problems. Optimal error estimates are obtained in one dimension and in multidimensions for Cartesian and triangular meshes. We extend the analysis to higher even-order equations and the linearized Cahn—Hilliard type equations. Numerical experiments are displayed to verify the theoretical results.

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