[en] The Kelvin-Helmholtz instability, caused by the sheared flow of fluids and plasmas, is of considerable practical importance. It may play a role in the edge turbulence associated with anomalous transport in the scrapeoff layer of tokamaks. Many features of this problem cause it to be one of the classic challenges to Computational Fluid Dynamics (CFD). The interesting behavior is localized to a narrow shear layer. For large Reynolds numbers, turbulence develops in this region, with thin ribbons of fluid interacting locally. In the incompressible limit, Poisson's equation must be solved for the stream function, along with the equation for convection of vorticity. Attempts to deal with the problem with adaptive and Lagrangian grids have a tendency to fail because the sheared flow can tear the grid apart. The authors treat the incompressible Kelvin-Helmholtz instability primarily as an interesting challenge in their development of the methods of Moving Finite Elements and Graph Massage as a general-purpose technique for difficult 2D problems in CFD. Moving Finite Elements provides a continuously adaptive motion of the unstructured triangular grid, concentrating it in regions of sharp gradients associated with the shear layer and the thin ribbons. Graph Massage allows the grid to break and reconnect occasionally, giving it the topological flexibility to avoid tangling. Periodic boundary conditions avoid interference of the boundaries with the flow, and Graph Massage allows one to take portions of the grid which flow out one side and put them back on the other side. The results now appear robust and believable. The 3D color movie shows vortices developing, merging, and circulating. The grid surges and boils around with the vortices with no difficulty. Vorticity is conserved to about 1 part in 1,000 for the duration of a long run at a Reynolds number of 1,000, with nonconservation of vorticity due primarily to Graph Massage rather than Moving Finite elements