# Local Discontinuous Galerkin methods for fractional diffusion equations

- Volume: 47, Issue: 6, page 1845-1864
- ISSN: 0764-583X

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topDeng, W. H., and Hesthaven, J. S.. "Local Discontinuous Galerkin methods for fractional diffusion equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.6 (2013): 1845-1864. <http://eudml.org/doc/273249>.

@article{Deng2013,

abstract = {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(hk + 1) uniformly across the continuous range between pure advection (β = 1) and pure diffusion (β = 2). In the two classic limits, known schemes are recovered. We discuss stability and present an error analysis for the space semi-discretized scheme, which is supported through a few examples.},

author = {Deng, W. H., Hesthaven, J. S.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {fractional derivatives; local discontinuous Galerkin methods; stability; convergence; error estimates},

language = {eng},

number = {6},

pages = {1845-1864},

publisher = {EDP-Sciences},

title = {Local Discontinuous Galerkin methods for fractional diffusion equations},

url = {http://eudml.org/doc/273249},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Deng, W. H.

AU - Hesthaven, J. S.

TI - Local Discontinuous Galerkin methods for fractional diffusion equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 6

SP - 1845

EP - 1864

AB - 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(hk + 1) uniformly across the continuous range between pure advection (β = 1) and pure diffusion (β = 2). In the two classic limits, known schemes are recovered. We discuss stability and present an error analysis for the space semi-discretized scheme, which is supported through a few examples.

LA - eng

KW - fractional derivatives; local discontinuous Galerkin methods; stability; convergence; error estimates

UR - http://eudml.org/doc/273249

ER -

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