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research article

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

Qiu, Liangliang
•
Deng, Weihua
•
Hesthaven, Jan S.  
2015
Journal of Computational Physics

This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with tri- angular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial discretization by the use of high-order nodal basis, employ- ing 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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DG2D_Frac.pdf

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