IJPAM: Volume 23, No. 3 (2005)

FINITE ELEMENT GALERKIN SOLUTIONS FOR
THE NONLINEAR FREE SURFACE PROBLEMS

S.K. Chung$^1$, K.I. Kim$^2$
$^{1,2}$Department of Mathematical Education
Seoul National University
Sillim-dong, Gwanak-gu, Seoul, 151-748, KOREA
$^1$e-mail: chung@plaza.snu.ac.kr
$^2$e-mail: shinjee0@snu.ac.kr


Abstract.Numerical computations for the water-wave free surface problem have been extensively studied. But the corresponding numerical analysis have been rarely worked out because of nonlinearity of free surface conditions. We discuss the numerical solutions of a semi-discrete finite element Galerkin method and a Crank-Nicolson type fully discrete one to solve the water-wave problem. Their stability and convergence are discussed and the error estimate of the potential function is expressed in terms of the kinematic free boundary and the potential function on the free boundary given by the Bernoulli's condition.

Received: August 1, 2005

AMS Subject Classification: 65N30, 35R35

Key Words and Phrases: free surface problem, finite element method, stability, error estimates, convergence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 23
Issue: 3