An unfitted hybridizable discontinuous galerkin method in shape optimization.
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Date
2022
Authors
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Journal ISSN
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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 para optar al título profesional de Ingeniero Civil Matemático.
Keywords
Ecuaciones Diferenciales, Métodos de Galerkin, Polinomios