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Mathematics of Computation

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A conservative finite element method for the Korteweg-deVries equation

Author: Ragnar Winther
Journal: Math. Comp. 34 (1980), 23-43
MSC: Primary 65N30; Secondary 35Q20
MathSciNet review: 551289
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Abstract: A finite element method for the 1-periodic Korteweg-de Vries equation

$\displaystyle {u_t} + 2u{u_x} + {u_{xxx}} = 0$

is analyzed. We consider first a semidiscrete method (i.e., discretization only in the space variable), and then we analyze some unconditionally stable fully discrete methods. In a special case, the fully discrete methods reduce to twelve point finite difference schemes (three time levels) which have second order accuracy both in the space and time variable.

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Article copyright: © Copyright 1980 American Mathematical Society

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