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We propose two families of mixed finite elements for solving the classicalHellinger-Reissner mixed problem of the linear elasticity equations in threedimensions. First, a family of conforming mixed triangular prism elements isconstructed by product of elements on triangular meshes and elements in onedimension. The well-posedness is established for all elements with $k\geq1$,which are of $k+1$ order convergence for both the stress and displacement.Besides, a family of reduced stress spaces is proposed by dropping the degreesof polynomial functions associated with faces. As a result, the lowest orderconforming mixed triangular prism element has 93 plus 33 degrees of freedom oneach element. Second, we construct a new family of nonconforming mixedtetrahedral elements. The shape function spaces of our stress spaces aredifferent from those of the elements in literature.

Conforming mixed triangular prism and nonconforming mixed tetrahedral elements for the linear elasticity problem