Based On A Variational Moving Mesh Point Boundary Value Problems With Computational Fluid

More and more complex nonlinear problems appear in Modem Science and Technology, with large gradients or discontinues in local region. To approximate the solution accurately in these regions, it is often necessary to generate a mesh that is dense where the solution is changing rapidly. Also, for the reason of efficiency, the mesh should be sparse where the solution is smooth. Moving mesh method is just the method. It makes the nodes' distributing depends on the solution's feature. In evolutionary PDE, the mesh should change with the solution. Obviously, it is an effective method to solve them.In this dissertation, we get a new moving mesh method. It is based on the idea that themesh should adapt the solution and should be smooth. A minimization of the function,, is introduced to govern the nodes' distribution. We solve itsEuler-Lagrange equation, u_xu_xxx_ξ² + (u_x² + a)x_ξξ =0, numerically to get the adaptation. Whyand how to form the new method is introduced in details. We make a numerical test in two points boundary problems with good result. At last, we solve one dimension fluid mechanics equations with our method and get satisfying result.