线性双曲守恒律的二阶显式TVD Runge-Kutta间断Galerkin方法的稳定性分析

Stability analysis of second-order explicit TVDRunge-Kutta discontinuous Galerkin methodfor linear hyperbolic conservation laws

利用二阶显式TVD Runge-Kutta间断Galerkin方法求解α阶差商下的线性双曲守恒律方程的稳定性问题。在方程的解充分光滑的情况下,通过有限元分析的方法,在理论上严格地证明了对于任意非均匀正则网格和k次分段多项式间断有限元空间。当CFL条件取为τ≤λC-2h时,算法是L2模稳定的,其中C和λ是与h和τ无关的常数。

The stability problem of the second-order explicit TVD Runge-Kutta discontinuous Galerkin method to solve the linear hyperbolic conservation law equations under the α-th order divided differences is studied. When the solution is sufficiently smooth, it is shown by the finite element analysis technique that for any k-th order piecewise polynomial space on the non-uniform regular meshes, the algorithm is L2-norm stable under the CFL condition τ≤λC-2h, where C and λ are constants independent of h and τ.