Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells
Finite element semidiscrete approximations on nonlinear dynamic shallow shell models in considered. It is shown that the algorithm leads to global, optimal rates of convergence. The result presented in the paper improves upon the existing literature where the rates of convergence were derived for small initial data only .
Mathematical Modelling and Numerical Analysis
Lasiecka, I., & Marchand, R. (2000). Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells. Mathematical Modelling and Numerical Analysis, 34 (1), 63-84. https://doi.org/10.1051/m2an:2000131