Lagrangian Finite Element Method for the 2-D Euler Equations

摘要

A grid free Lagrangian finite element method is introduced for the 2-Dincompressible Euler equations. The method is derived based on the observation that the product of the Biot-Savart kernel and polynomial can be integrated analytically over any triangle. This enables us to obtain a numerically Lagrangian method without using numerical smoothing. Moreover, we show that the method converges uniformly with second-order accuracy. Actually, we establish a l at infinity stability result which applies to kernels that are more singular than the Biot-Savart kernel, as long as the kernel is L 1 sub loc integrable. Another useful result is that we prove convergence of our method when using local regridding, which allows the method to run for longer time even with a fixed mesh. The second-order convergence is also illustrated by our numerical experiments. Reprints. (jhd)