Numerical solutions for nonlinear free surface flows by finite element methods

Numerical computations for the water-wave problem have been extensively studied. But the corresponding numerical analysis has not been worked out because of nonlinearity of free surface equation. We will discuss numerical stability and error estimates of an algorithm which uses finite element Galerkin method to solve the water-wave problem. In order to do that, we employ an extended Lax-Richtmyer equivalence theorem.