Discontinuous Galerkin spectral element methods for nonlinear reaction-diffusion equations are considered. The schemes are basically in the Legendre-Galerkin form. The nonlinear term is interpolated through the Chebyshev-Gauss-Lobatto points. The jump term tackled by the central numerical flux in space variation. The fourth-order low-storage Runge-Kutta scheme is applied for time discrete inside each subinterval. The methods can be used to solve discontinuous initial value problems and implemented in a parallel way. Stability and the optimal rate of convergence in L2-norm for the semi-discrete scheme are shown using the approximate results of the Chebyshev-Gauss-Lobatto interpolation operator without a weight function. Numerical results for the continuous and discontinuous problems are given.
WU Hua, HAN Xiao-Fei
. Discontinuous Galerkin Spectral Element Methods for Nonlinear Reaction-Diffusion Equations[J]. Journal of Shanghai University, 2014
, 20(6)
: 757
-768
.
DOI: 10.3969/j.issn.1007-2861.2013.07.029
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