Remeshing of Deformed Geometry

There's a deforming part in a geometry with an edge moving downsides and the others hoding their position.
After I defined the free deformation part and prescribed the mesh velocity, and run the model.
I can't satisfy with the result, the region connected to the unreformed parts are distort too much.
So how to re mesh the deforming mesh to couple with the deforming geometry during the calculation?