Space-time Legendre-Gauss-Lobatto collocation method for two-dimensional generalized sine-Gordon equation

作者：Shan, Yingying; Liu, Wenjie^*; Wu, Boying

来源：Applied Numerical Mathematics, 2017, 122: 92-107.

DOI：10.1016/j.apnum.2017.08.003

• Two-dimensional sine-Gordon equation
• Space-time Legendre-Gauss-Lobatto
• collocation method
• H-1 projection for collocation method
• Error estimates

In this paper, we present a space-time Legendre-Gauss-Lobatto (LGL) collocation method for solving the generalized two-dimensional sine-Gordon equation with nonhomogeneous Dirichlet boundary conditions. The proposed method is based on the LGL collocation method to discretize in space, then use the LGL collocation method or block LGL collocation method to discretize in time. Our formulation has high-order accuracy in both, space and time. We introduce a new H-1 projection for the error analysis of collocation method for nonhomogeneous Dirichlet boundary conditions. This projection differs from the classical H-1 projection. The new H-1 projection is identically equal to Lagrange interpolation on boundary. The approximation properties of the new H-1 projection are obtain. We derive error bounds in both discrete L-2 and H-1 norms for the (spatially) semidiscrete formulation, the analysis is based on new H-1 projection results.

• 出版日期2017-12
• 单位哈尔滨工业大学; 黑龙江大学