Método LDG para la ecuación de difusión fraccionaria en 1D

Alvarez Navarro, Michael A.

Publication

Método LDG para la ecuación de difusión fraccionaria en 1D

Alvarez Navarro, Michael A.

Abstract

This thesis describes an implementation of the Local Discontinuous Galerkin LDG method applied to a problem of fractional diffusion. The discrete formulation of the associated system is discussed, with emphasis on the construction of the fractional operator. A strategy is provided to add a term of stability in the primary variable, unlike other implementations that stabilize the method by penalizing in the auxiliary variable, in such a way that convergence order is obtained O (h p+1 ) for polynomials of degree p. Additionally, numerical experiments are shown in which little regularity is needed, on the part of the exact solution, to obtain optimum convergence.