# Undergraduate Thesis of Juan Manuel Cárdenas

Career | Mathematical Civil Engineering, Universidad de Concepción | |
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Enrollment Year | 2011 | |

Senior Year | 2018 | |

Thesis Title | A Discontinuous Hybridizable Galerkin Method for Linear Elasticity in Curved Domains | |

## Thesis Summary: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 | |

Professional Monitoring | ||

PDF Tesis | Download Thesis PDF | |

(No publications) |

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