dc.contributor |
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.contributor |
Fernández Méndez, Sonia |
dc.contributor |
Discacciati, Marco |
dc.contributor.author |
Oliver Parera, Maria |
dc.date |
2013-07 |
dc.identifier.uri |
http://hdl.handle.net/2099.1/19376 |
dc.language.iso |
eng |
dc.publisher |
Universitat Politècnica de Catalunya |
dc.rights |
Attribution-NonCommercial-ShareAlike 3.0 Spain |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.rights |
http://creativecommons.org/licenses/by-nc-sa/3.0/es/ |
dc.subject |
Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject |
Fluid mechanics |
dc.subject |
Hybridizable Galerkin method |
dc.subject |
Darcy Stokes problem |
dc.subject |
Mecànica de fluids |
dc.subject |
Classificació AMS::76 Fluid mechanics::76S05 Flows in porous media; filtration; seepage |
dc.title |
Discontinuous finite elements for coupled problems |
dc.title |
Elementos finitos discontinuos para problemas acoplados |
dc.type |
info:eu-repo/semantics/masterThesis |
dc.description.abstract |
El objetivo de este trabajo es estudiar las propiedades de formulaciones de elementos finitos para problemas acoplados Darcy-Stokes basadas en HDG.Las tareas a elegir entre los estudiantes y los supervisores son: colaborar en la propuesta y análisis de nuevas formulaciones para el problema acoplado, demostrando teoremas de convergencia y estabilidad, olaborar en la adaptación del código de elementos finitos HDG disponible para Darcy, para el tratamiento del problema acoplado, estudiar mediante ejemplos numéricos las propiedades de convergencia y estabilidad |
dc.description.abstract |
The ltration of
uids through porous media is a challenging problem with many
relevant applications in ltration problems, such as the ltration of blood through
arterial vessel walls or the ltration of water through sand.
To model this problem we consider di erent systems of partial di erential equations
on each domain: in the free domain we will use Stokes equations, while the
uid
in the porous domain is modelled using Darcy equations. In the free domain the
uid is discretized by the Continuous Galerkin method, but in the porous domain
we will use de Hybridizable Discontinuous Galerkin method.
The project is focused in the Hybridizable Discontinuous Galerkin method, which
is a new method that combines the advantatges of the Discrete Galerkin methods
with the computational e ciency of the Continuous Galerkin methods. The main
advantatges of this method are:
Reduced number of degrees of freedom. With the hybridization process we can
reduce the number of degrees of freedom at the boundaries of each element.
Optimal convergence. It converges with order k + 1 in the L2 norm, where
k is the degree of the polynomials used to approximate the solution. This
convergence is for the solution and the derivative of the solution.
Superconvergence and local postprocessing. The method alloes us to use an
element-by-element postprocessing to obtain a new and better approximation
with order k + 2, for k 1.
The structure of the project is as follows. At the rst Chapter we set the problem:
the equations that we will use and the boundary conditions. Next Chapter is
dedicated to the Hybridizabe Galerkin method and to the analysis of the error of
this method, for this Chapter we referenciate to [1], [3], [4], [7], [5]. We continue
with a Chapter dedicated to the coupling, where we remark the article [6]. And
nally we apply our problem to the ltration of water through sand. |