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A conforming triangular mixed element recently proposed by Hu and Zhang forlinear elasticity is extended by rearranging the global degrees of freedom.More precisely, adaptive meshes $\mathcal{T}_1$, $\cdots$, $\mathcal{T}_N$which are successively refined from an initial mesh $\mathcal{T}_0$ through anewest vertex bisection strategy, admit a crucial hierarchical structure,namely, a newly added vertex $\boldsymbol{x}$ of the mesh $\mathcal{T}_\ell$ isthe midpoint of an edge $e$ of the coarse mesh $\mathcal{T}_{\ell-1}$. Such ahierarchical structure is explored to partially relax the $C^0$ vertexcontinuity of symmetric matrix-valued functions in the discrete stress space ofthe original element on $\mathcal{T}_\ell$ and results in an extended discretestress space. A feature of this extended discrete stress space is itsnestedness in the sense that a space on a coarse mesh $\mathcal{T}$ is asubspace of a space on any refinement $\hat{\mathcal{T}}$ of $\mathcal{T}$,which allows a proof of convergence of a standard adaptive algorithm. The ideais extended to impose a general traction boundary condition on the discretelevel. Numerical experiments are provided to illustrate performance on bothuniform and adaptive meshes.

Partial relaxation of C^0 vertex continuity of stresses of conforming mixed finite elements for the elasticity problem