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arXiv · 1604.07903

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

Jun Hu·Rui Ma
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Abstract

We propose two families of mixed finite elements for solving the classical Hellinger-Reissner mixed problem of the linear elasticity equations in three dimensions. First, a family of conforming mixed triangular prism elements is constructed by product of elements on triangular meshes and elements in one dimension. 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 degrees of polynomial functions associated with faces. As a result, the lowest order conforming mixed triangular prism element has 93 plus 33 degrees of freedom on each element. Second, we construct a new family of nonconforming mixed tetrahedral elements. The shape function spaces of our stress spaces are different from those of the elements in literature.

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Jun Hu, Rui Ma. 2016-04-27. Conforming mixed triangular prism and nonconforming mixed tetrahedral elements for the linear elasticity problem. https://arxiv.org/abs/1604.07903

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