Lagrangian Mixed Finite Element Methods for Nonlinear Thin Shell Problems

Abstract

© 2019 Walter de Gruyter GmbH, Berlin/Boston 2019. A class of Lagrangian mixed finite element methods is constructed for an approximate solution of a problem of nonlinear thin elastic shell theory, namely, the problem of finding critical points of the functional of potential energy according to the Budiansky-Sanders model. The proposed numerical method is based on the use of the second derivatives of the deflection as auxiliary variables. Sufficient conditions for the solvability of the corresponding discrete problem are obtained. Accuracy estimates for approximate solutions are established. Iterative methods for solving the corresponding systems of nonlinear equations are proposed and investigated.