四阶线性方程的隐显式全离散局部间断Galerkin方法
Implicit-Explicit Fully Discrete Local Discontinuity Galerkin Method for Fourth-Order Linear Equations
摘要: 针对一维四阶线性方程，研究了一种隐显式Runge-Kutta全离散局部间断Galerkin方法的稳定性和最优误差估计。空间离散采用局部间断Galerkin方法，时间离散选用强稳定显式Runge-Kutta方法和具有L稳定对角隐式Runge-Kutta方法相结合的三阶隐显式Runge-Kutta方法，数值流通量采用广义交替数值流通量，从而得到全离散LDG格式，分析了该格式的稳定性，同时引入全局Gauss-Radau投影，证明该格式具有 k+1 阶收敛。最后通过数值实验验证理论结果的正确性。
Abstract: The stability and error estimation of an implicit-explicit Runge-Kutta fully discrete local discontinuous Galerkin method for one-dimensional fourth-order linear equations are studied. The local discontinuity Galerkin method is used for spatial discretization, and the third-order implicit-explicit Runge-Kutta method combining the strong-stability-preserving explicit Runge-Kutta method and the implicit Runge-Kutta method with L-stable diagonal implicit is used for time marching, and the numerical circulation adopts the generalized alternating numerical flux, so as to obtain the fully discrete LDG scheme, and the stability of the scheme is analyzed, and the generalized Gauss-Radau projection is introduced to prove that the scheme has k+1 order convergence. Finally, the theoretical results are verified by numerical experiments.
文章引用：赵思敏, 宋灵宇. 四阶线性方程的隐显式全离散局部间断Galerkin方法[J]. 应用数学进展, 2025, 14(4): 437-452. https://doi.org/10.12677/aam.2025.144175

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