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

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.


Published in:
Journal of Computational Physics, 298, 678-694
Year:
2015
Publisher:
San Diego, Elsevier
ISSN:
0021-9991
Keywords:
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 Record created 2014-10-27, last modified 2018-09-13

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