An unfitted hybridizable discontinuous galerkin method in shape optimization.
Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad de Concepción
Abstract
Shape optimization seeks to optimize the shape of a region where certain partial differential equation is posed such that a functional of its solution is minimized/maximized. In this thesis we give an introduction to shape optimization through a model problem, introducing the concepts of shape derivative for a function and perturbation of the shape for a functional, we deduce the optimality conditions for the problem, and then we will present a numerical method to seek the solution via a hybridizable discontinuous Galerkin methods on curved domains. Subsequently, we develop a rigorous treatment to analyze the well-posedness of the problems that arise from the optimality conditions, and provide an a priori error analysis for each scheme.
Description
Tesis presentada para optar al título de Ingeniero Civil Matemático.
Keywords
Ecuaciones Diferenciales, Métodos de Galerkin, Polinomios