Scientific Computing Group Report - Detail view

Identifier: 2010-19

Author(s): W. Deng and J.S. Hesthaven

Title: Discontinuous Galerkin Method for Fractional Diffusion Equations

Page count: 23 pp.

Date: May 27, 2010

Abstract:

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(h^k+1) in the continuous range between pure advection (β = 1) and pure diffusion (β = 2). In these limits, known schemes are recovered. The analysis is confirmed through a few examples.

BibTeX:

@techreport{brown_sc_2010_19,
  title = "{Discontinuous Galerkin Method for Fractional Diffusion Equations}",
  author = "W. Deng and J.S. Hesthaven",
  institution = "Scientific Computing Group, Brown University",
  number = "2010-19",
  address = "Providence, RI, USA",
  year = 2010,
  month = may,
}

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