A Coupling Method of Mixed and Lagrange Finite Elements for Linear Elasticity Problem
For computational mechanics researchers, this method offers a practical way to improve stress accuracy in critical regions without excessive computational cost.
The paper proposes a finite element method coupling mixed and Lagrange elements to capture stress concentrations in elasticity problems, achieving a balance between stress accuracy and computational efficiency. Optimal error estimates are established and verified numerically.
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress concentration, while standard Lagrange elements are used elsewhere, achieving a balance between stress accuracy and computational efficiency. The well-posedness of the coupled formulation and optimal a priori error estimates are established, even when the size of the mixed finite element subregion is $O(h)$. Numerical experiments are presented to verify the theoretical convergence rates and to demonstrate the effectiveness and efficiency of the proposed method.