In this work, we aim to develop efficient numerical schemes for a nonlinear fourth-order partial differential equation arising from the so-called dynamic Gao beam model. We use C0 interior penalty finite element methods over the spatial domain to set up the semi-discrete formulations. Convergence results for the semi-discrete case are shown, based on a truncated variational formulation and its equivalent abstract formulations. We combine time discretizations to derive fully discrete numerical formulations. Newton's method is applied to compute one time step numerical solutions of a nonlinear system. Two numerical examples are provided: one supports our theoretical results and the other presents a buckling state of the Gao beams.
Bibliographical noteFunding Information:
The research of EJP was supported in part by NRF , South Korea under grant nos. 2015R1A5A1009350 and 2016R1A2B4014358 .
The research of EJP was supported in part by NRF, South Korea under grant nos. 2015R1A5A1009350 and 2016R1A2B4014358.
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All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics