Stability Analysis of the Explicit Ｒunge-Kutta Local Discontinuous Galerkin Method - BI Hui; QIAN Chen-geng (Journal of Harbin University of Science and Technology)
To analyze the stability of the local discontinuous Garlerkin method for heat equation，where the time discretization is the explicit TVD Ｒunge-Kutta method. For the sufficiently smooth solution case，when the finite element space is the k-th order piecewise polynomial space on the regular meshes，we use the finite element analysis technique to proof the L2-norm stability for hear equation under the CFL condition τ≤λμ － 2h2，where τ，h are the time step and the length of the element respectively，and μ，λ are constants independent of h，τ.