Solano Palma, ManuelSánchez Vizuet, TonatiuhHenríquez Novoa, Esteban Ignacio2022-12-212024-05-152024-08-282022-12-212024-05-152024-08-282022https://repositorio.udec.cl/handle/11594/10496Tesis para optar al título profesional de Ingeniero Civil Matemático.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.engCreative Commoms CC BY NC ND 4.0 internacional (Atribución-NoComercial-SinDerivadas 4.0 Internacional)Ecuaciones DiferencialesMétodos de GalerkinPolinomiosTesis