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 triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial discretization by the use of high-order nodal basis, employing m...

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Bibliographic Details
Published inJournal of computational physics Vol. 298; pp. 678 - 694
Main Authors Qiu, Liangliang, Deng, Weihua, Hesthaven, Jan S.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2015
Subjects
2D fractional diffusion equation
Convergence
Diffusion
Galerkin methods
Mathematical analysis
Mathematical models
Nodal discontinuous Galerkin methods
Optimization
Polynomials
Triangular meshes
Two dimensional
Nodal discontinuous Galerkin methods
Triangular meshes
2D fractional diffusion equation
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Summary: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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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2015.06.022