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arXiv · 1410.0796

Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshes

Liangliang Qiu·Weihua Deng·Jan Hesthaven
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Abstract

This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial discretization by the use of high-order nodal basis, employing multivariate Lagrange polynomials defined on the triangles. Stability analysis and error estimates are provided, which shows that if polynomials of degree $N$ are used, the methods are (N+1)-th order accurate for general triangulations. Finally, the performed numerical experiments confirm the optimal order of convergence.

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Liangliang Qiu, Weihua Deng, Jan Hesthaven. 2014-10-03. Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshes. https://doi.org/10.1016/j.jcp.2015.06.022

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