  We show numerical results of triangular cavity flow problems solved by a
Lagrange-Galerkin scheme free from numerical quadrature. The scheme has
recently developed by us, where a locally linearized velocity and the backward
Euler approximation are used in finding the position of fluid particle at the
previous time step. Since the scheme can be implemented exactly as it is, the
theoretical stability and convergence results are assured, while the
conventional Lagrange-Galerkin schemes may encounter the instability caused by
numerical quadrature errors. The scheme is employed to solve cavity flow
problems in triangular domains, where we observe the bifurcation of stationary
solutions and the patterns of streamlines.
