Optimal second order rectangular elasticity elements with weakly symmetric stress
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We present new second order rectangular mixed finite elements for linear elasticity where the symmetry condition on the stress is imposed weakly with a Lagrange multiplier. The key idea in constructing the new finite elements is enhancing the stress space of the Awanou's rectangular elements (rectangular Arnold-Falk-Winther elements) using bubble functions. The proposed elements have only 18 and 63 degrees of freedom for the stress in two and three dimensions, respectively, and they achieve the optimal second order convergence of errors for all the unknowns. We also present a new simple a priori error analysis and provide numerical results illustrating our analysis.
|Number of pages||21|
|Journal||BIT Numerical Mathematics|
|Publication status||Published - 2014|
|MoE publication type||A1 Journal article-refereed|
- Elasticity, Mixed finite element, Rectangular finite element, Weakly imposed symmetry