Some remarks on moving finite element methods (Q1059380)

The object of this paper is to justify the moving finite element method in the context of the minimum-residual technique. The authors have pointed out the essential difference between one and multi-dimensional cases and have shown that under certain regularity conditions imposed on the mesh distribution and forced by penalty factors, the moving finite element method is equivalent to the minimum residual technique. Thus the formal differentiation with respect to the solution and mesh deformation rates in the \(L^ 2\)-residual makes sense.