Numerical methods for static shallow shells lying over an obstacle

Paolo Piersanti; Xiaoqin Shen

doi:10.1007/s11075-019-00830-7

Numerical methods for static shallow shells lying over an obstacle

Numer Algorithms. 2020;85(2):623-652. doi: 10.1007/s11075-019-00830-7. Epub 2020 Jan 10.

Authors

Paolo Piersanti¹, Xiaoqin Shen²

Affiliations

¹ Institute of Mathematics and Scientific Computing, Karl-Franzens-Universität Graz, Heinrichstraße 36, A8010 Graz, Austria.
² Department of Mathematics, School of Sciences, Xi'an University of Technology, P.O. Box 1243, Yanxiang Road No. 58, Xi'an, 710054 Shaanxi Province China.

Abstract

In this paper, a finite element analysis to approximate the solution of an obstacle problem for a static shallow shell confined in a half space is presented. To begin with, we establish, by relying on the properties of enriching operators, an estimate for the approximate bilinear form associated with the problem under consideration. Then, we conduct an error analysis and we prove the convergence of the proposed numerical scheme.

Keywords: Elliptic variational inequalities; Enriching operator; Nonconforming finite element method; Obstacle problems; Shallow shell.