A new priori error estimation of nonconforming element for two-dimensional linearly elastic shallow shell equations

Abstract

In this paper, we mainly propose a new priori error estimation for the two-dimensional linearly elastic shallow shell equations, which rely on a family of Kirchhoff–Love theories. As the displacement components of the points on the middle surface have different regularities, the nonconforming element for the discretization shallow shell equations is analysed. Then, relying on the enriching operator, a new error estimate of energy norm is given under the regularity assumption $\vec{\zeta}_H \times \zeta_3 \in (H^{1+m} (\omega))^2 \times H^{2+m} (\omega)$ with any $m \gt 0$. Compared with the classic error analysis in other shell literature, convergence order of numerical solution can be controlled by its corresponding approximation error with an arbitrarily high order term, which fills the gap in the computational shell theory. Finally, numerical results for the saddle shell and cylindrical shell confirm the theoretical prediction.