  A finite element method for solving nonlinear differential equations on a
grid, with potential applicability to computational fluid dynamics (CFD), is
developed and tested. The current method facilitates the computation of
solutions of a high polynomial degree on a grid. A high polynomial degree is
achieved by interpolating both the value, and the value of the derivatives up
to a given order, of continuously distributed unknown variables. The
two-dimensional lid-driven cavity, a common benchmark problem for CFD methods,
is used as a test case. It is shown that increasing the polynomial degree has
some advantages, compared to increasing the number of grid-points, when solving
the given benchmark problem using the current method. The current method yields
results which agree well with previously published results for this test case.
