Método LDG para la ecuación de difusión fraccionaria en 1D

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.