High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Difusion Equation

doi:10.1007/s42967-019-00058-1

Abstract

Abstract: In this article, some high-order local discontinuous Galerkin (LDG) schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimensional nonlinear fractional difusion equation. The unconditional stability of the LDG scheme is proved, and an a priori error estimate with O(h^k+1 + △t²) is derived, where k ≥ 0 denotes the index of the basis function. Extensive numerical results with Q^k(k=0, 1, 2, 3) elements are provided to confrm our theoretical results, which also show that the secondorder convergence rate in time is not impacted by the changed parameter θ.

Key words: Two-dimensional nonlinear fractional difusion equation, High-order LDG method, Second-order θ scheme, Stability and error estimate

CLC Number:

65M60
65N30

Min Zhang, Yang Liu, Hong Li. High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Difusion Equation[J]. Communications on Applied Mathematics and Computation, 2020, 2(4): 613-640.

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References

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