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Solution of Second Order Elliptic Equations on Polygonal/Polyhedral Meshes by the Virtual Element Method with Applications in Geosciences

Federica Milinanni

Solution of Second Order Elliptic Equations on Polygonal/Polyhedral Meshes by the Virtual Element Method with Applications in Geosciences.

Rel. Stefano Berrone, Marco Verani. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Matematica, 2020

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Abstract:

The reaction-convection-diffusion equation is a second order elliptic partial differential equation that can be used to model many different physical phenomena. A method to solve this class of problems is the Virtual Element Method (VEM). In this thesis we focus on two dimensional problems defined on polygonal meshes, considering both the stationary and evolutive case. The aim of this thesis is to analyze and implement the stabilization methods Streamline Upwind Petrov-Galerkin (SUPG) and Mass Lumping in the particular case of Virtual Element space of order k = 1. Numerical results show the positive stabilization effect of SUPG and Mass Lumping when the problem is characterized respectively by very large P├ęclet and very low Karlowitz numbers. Moreover, an error analysis on an easy stationary problem shows that the stabilization methods preserve the rate of convergence of VEM. Finally, a simulation of a realistic geophysical evolutive problem is carried out to show the performance of the method on a domain characterized by a high geometrical complexity.

Relators: Stefano Berrone, Marco Verani
Academic year: 2019/20
Publication type: Electronic
Number of Pages: 81
Subjects:
Corso di laurea: Corso di laurea magistrale in Ingegneria Matematica
Classe di laurea: New organization > Master science > LM-44 - MATHEMATICAL MODELLING FOR ENGINEERING
Ente in cotutela: KUNGLIGA TEKNISKA HOGSKOLAN (ROYAL INSTITUTE OF TECHNOLOGY) - SCI (SVEZIA)
Aziende collaboratrici: UNSPECIFIED
URI: http://webthesis.biblio.polito.it/id/eprint/14784
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