Error estimations of mixed finite element methods for nonlinear problems of shallow shell theory

11th International Conference on "Mesh methods for boundary-value problems and applications"

Karchevsky, M.^1

Department of Computational Mathematics, Institute of Computational Mathematics and Information Technologies, Kazan Federal University, 18 Kremlyovskaya Street, Kazan

420008, Russia^1

关键词: Approximate solution;    Auxiliary variables;    Mixed finite element methods;    Non-linear theory;    Nonlinear problems;    Second derivatives;    Shallow shells;    Variational formulation;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012048/pdf
DOI  :  10.1088/1757-899X/158/1/012048

来源: IOP

【 摘 要 】

The variational formulations of problems of equilibrium of a shallow shell in the framework of the geometrically and physically nonlinear theory by boundary conditions of different main types, including non-classical, are considered. Necessary and sufficient conditions for their solvability are derived. Mixed finite element methods for the approximate solutions to these problems based on the use of second derivatives of the bending as auxiliary variables are proposed. Estimations of accuracy of approximate solutions are established.