Local discontinuous Galerkin methods for fractional ordinary differential equations

Local discontinuous Galerkin methods for fractional ordinary differential equations

This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs). The natural upwind choice of the numerical fluxes for the initial value problem for FODEs ensures stability of the methods. The solution can be computed element by element with optimal order of convergence k+ 1 in the L2 norm and superconvergence...

Local Discontinuous Galerkin Methods for Fractional Diffusion Equations

We consider the development and analysis of local discontinuous Galerkin methods for fractional diffusion problems in one space dimension, characterized by having fractional derivatives, parameterized by β ∈ [1, 2]. After demonstrating that a classic approach fails to deliver optimal order of convergence, we introduce a modified local numerical flux which exhibits optimal order of convergence O...

Discontinuous Galerkin Methods for Fractional Diffusion Equations

We consider the development and analysis of local discontinuous Galerkin methods for fractional diffusion problems, characterized by having fractional derivatives, parameterized by β ∈ [1, 2]. We show through analysis that one can construct a numerical flux which results in a scheme that exhibit optimal order of convergence O(hk+1) in the continuous range between pure advection (β = 1) and pure...

Discontinuous Galerkin Methods for Partial Differential Equations

Day 1: Monday, September 26, 2011 Hybridized DG Method and Mimetic Finite Differences Franco Brezzi IUSS and IMATI-CNR, Pavia Via Ferrata 1, 27100 Pavia [email protected] Abstract: The talk will discuss the relationships between certain variants of Mimetic Finite Differences and the Hybridized version of DG methods for some very simple model problem. The talk will discuss the relationships be...

Fuzzy Local Fractional Differential Equations