Undergraduate Thesis of Juan Manuel Cárdenas
|Career||Mathematical Civil Engineering, Universidad de Concepción|
|Thesis Title||A Discontinuous Hybridizable Galerkin Method for Linear Elasticity in Curved Domains|
This work proposes a hybridize discontinuous Galerkin (HDG) method for the linear elasticity problem in domains Ω that are not necessarily polyhedral/polygonal. In particular, we approximate the domain by a polyhedral/polygonal computational domain Dh where the HDG solution can be computed. The Dirichlet boundary data is suitable transferred from the boundary Γ := ∂Ω to the computational boundary Γh := ∂Dh. We show that the scheme is well-posed. Moreover, we prove a priori error estimates showing that the method is optimal. In addition, we prove that the numerical trace is superconvergent with order k + 2 if the distance between Γ and Γh is of order h 2 . On the other hand, if this distance is of order h, then the numerical trace superconvergences with rate k + 3/2. We validate our theoretical results with numerical experiments in two-dimension.
|Thesis Director(s)||Manuel Solano|
|Thesis Project Approval Date||2017, April 24|
|Thesis Defense Date||2018, March 26|
|PDF Tesis||Download Thesis PDF|