Estudio del método de Galerkin discontinuo nodal aplicado a la ecuación de advección lineal 1D
The present work focuses on Nodal Discontinuous Galerkin Method applied to the one-dimensional linear advection equation, which approximates the global solution, partitioning its domain into elements. In each element the local solution is approximated by using interpolation in such a way that the...
| Autor Principal: | Sosa Alva, Julio César |
|---|---|
| Formato: | Tesis de Maestría |
| Idioma: | Español |
| Publicado: |
Pontificia Universidad Católica del Perú
2019
|
| Materias: | |
| Acceso en línea: |
http://repositorio.pucp.edu.pe/index/handle/123456789/134997 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: |
The present work focuses on Nodal Discontinuous Galerkin Method applied to the one-dimensional
linear advection equation, which approximates the global solution, partitioning its domain into elements.
In each element the local solution is approximated by using interpolation in such a way that
the total numerical solution is a direct sum of those approximations (polynomials). This method
aims at reaching a high order through a simple implementation. This model is studied by Hesthaven
and Warburton [16], with the particularity of Joining the best of the Finite Volumes Method and
the best of Finit Element Method .
First, the main results are revised in detail concerning the Jacobi orthogonal polynomials; more
precisely, its generation formula and other results which help implementing the method. Concepts
regarding interpolation and best approximation are studied. Furthermore, some notions about Sobolev
space interpolation is revised. Secondly, theoretical aspects of the method are explained in
detail , as well as its functioning. Thirdly, both the two method consistency theorems (better approximation
and interpolation), proposed by Canuto and Quarteroni [4], and error behavior theorem
based on Hesthaven and Warburton [16] are explained in detail. Finally, the consistency theorem
referred to the interpolation is veri ed numerically through the usage of the Python language as
well as the error behavior. It is worth mentioning that, from our numerical results, we propose a
new bound for the consistency (relation 4.2 (4.2)), whose demonstration will remain for a future
investigation. |
|---|