Open Access Dissertation
Date of Award
In this work, theory background of the sobolev spaces and finite element spaces are
reviewed first. Then the details of how the thermoelastic Kirchhoff-Love(KL) plates numerically established are presented. Later we approaches to the thermoelastic KL system numerically with mixed element method, H^1−Galerkin method and interior penalty discontinuous galerkin method(IP-DG).
What is more, the SIP-DG also applied to solve this KL system numerically. The well-posedness, existence, uniqueness and convergence properties are theoretical analyzed. The gain of the convergence rate is also O(h^k), that is 1 less than the observed convergence rate.
When discussing the H1-Galerkin method, the main advantages over traditional mixed element method, is LBB condition naturally inherent. It is proved that the existence and uniqueness of solutions for such discrete scheme. Furthermore, the semi discrete and fully discrete error estimates details are proposed to show the theoretical convergence rate is O(h^k), which is also 1 lesser than the observed convergence rate O(h^k). And optimal convergence rate can be obtained only for some variables.
Zhou, Zeyu, "Numerical Approaches To A Thermoelastic Kirchhoff-Love Plate System" (2019). Wayne State University Dissertations. 2250.