A conservative finite element method for the Korteweg-de Vries equation

Winther, Ragnar

doi:10.1090/S0025-5718-1980-0551289-5

A conservative finite element method for the Korteweg-de Vries equation
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Math. Comp. 34 (1980), 23-43 Request permission

Abstract:

A finite element method for the 1-periodic Korteweg-de Vries equation \[ {u_t} + 2u{u_x} + {u_{xxx}} = 0\] 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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