A Conservative Finite Element Method for the Korteweg-de Vries Equation

@inproceedings{Winther2010ACF,
  title={A Conservative Finite Element Method for the Korteweg-de Vries Equation},
  author={Ragnar Winther},
  year={2010}
}
A finite element method for the 1-periodic Korteweg-de Vries equation "t + 2uux + "xxx = ° 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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