## Abstract

We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order (Formula presented.) with (Formula presented.). For exact time-marching, we derive optimal algebraic error estimates assuming that the exact solution is sufficiently regular. Thus, if for each time (Formula presented.)∈[0,T] the approximations are taken to be piecewise polynomials of degree (Formula presented.) on the spatial domain (Formula presented.), the approximations to u in the (Formula presented.)-norm and to ∇u in the (Formula presented.)-norm are proven to converge with the rate (Formula presented.), where h is the maximum diameter of the elements of the mesh. Moreover, for k≥1 and quasi-uniform meshes, we obtain a superconvergence result which allows us to compute, in an elementwise manner, a new approximation for u converging with a rate of (Formula presented.).

Original language | English (US) |
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Pages (from-to) | 293-314 |

Number of pages | 22 |

Journal | Numerische Mathematik |

Volume | 130 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2015 |

## Keywords

- 26A33
- 35L65
- 65M12
- 65M15
- 65M60
- 65N30