APPROXIMATIONS OF THE KDV EQUATION BY LEAST-SQUARES FINITE-ELEMENTS

The problem of approximating solutions to the Korteweg-de Vries (KdV) equation is investigated using a least squares finite element method. The third order KdV equation is recast as a first-order system and a least-squares finite element approach is introduced for the semidiscrete time-differenced form of the resulting equations. Of particular interest are the approximation properties for solitary wave solutions (solitons). We examine the amplitude and phase error for a representative test problem as well as other examples including the passage of one soliton through another.