Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM (Q1740632)

Mixed finite element schemes, in particular the symmetric Arnold-Winther scheme for linear elasticity, are studied and a posteriori error analyses are performed for the nonconforming residual. The obtained explicit error estimator is shown to be reliable and efficient. The linear elastic model problem considers a simply connected bounded Lipschitz domain and a shape regular triangulation is applied. The proposed explicit error estimator depends on the Green strain approximation and its piecewise derivatives and jumps across the edges. Adaptive mesh refining is implemented, showing the efficiency of the error estimator. Different benchmark computations illustrate the robustness and efficiency for fourth-order convergence. The analysis is restricted to the two-dimensional case. Finally, the appendices discuss the improved convergence order and explain the successful treatment of incompatible Neumann data.