Elasticity Of Mixed Finite Element Format

The finite element method of elasticity problem is one of the most frequently used techniques to approximate the solution of the equations. By the form which is different from the traditional variational forms, c~0 -triangular element ,c~0-tetrahedral element, c~0-rectanglular element, c~0-cubic element and Adini element are analysed in the paper.Compared with traditional methods, these methods is relatively easy. Far more important, these methods adapt to not only the plane elasticity problem but also to practical problem on the three dimension.Arnold once said it's difficult to extend to three dimension. We extend the results to the three-dimensional linear elasticity.Using the first Korn inequation in this paper, we prove the version of Korn's inequality hold in the finite element space.Then we can use Babuska-Brezzi theory to get error estimates.At the same time, the order of error estimates is extended from one to arbitrary.