Abstract:

This talk will describe a new adaptive method of solving non-linear parabolic PDEs with moving boundaries, using a moving mesh with finite elements. The approach is based upon conserving the distribution of two monitor functions across the spatial domain throughout time, the first driving the velocity of the internal nodes in the moving mesh, the second the boundary nodes, and can allow for non-linear monitor functions. The benefits of using two monitor functions will be discussed, and a number of computational examples will be presented, using a variety of monitor functions, when applied to an example non-linear parabolic PDE. The computational accuracy of these schemes will be assessed and the effect of the different monitor functions on mesh movement will be discussed.