Comparison of Finite-Element and Finite-Difference Schemes. Part II: Two-Dimensional Gravity Wave Motion

Abstract

Irregular grid finite-difference techniques lead to equations similar to those obtained using finite-element techniques. The simpler finite-difference equations offer the advantage of greater computational economy. The time-implicit finite-element equations must be inverted at each time step, and the maximum size of the time step is only half that which can be used with the finite-difference equations. Both techniques result in instabilities when used with highly irregular grids, and the finite-element equations are also unstable if the basin depth is variable. Although the finite-element results are better when compared with finite-difference results from the same grid, comparable finite-difference results can be obtained using a finer grid at less computational expense.