Analysis of fully discrete approximations for dissipative systems and its applications
摘要：In this talk, we present a numerical analysis of fully discrete approximations for general dissipative systems. We introduce a class of implicit Runge-Kutta methods satisfying two conditions as the time discretization methods. Under these two conditions with the dissipative condition, we can obtain the energy boundedness and a priori error estimates. Then we consider a specific dissipative system, i.e. time-dependent nonlocal diffusion problems, with the discontinuous Galerkin discretization in space. It is very convenient to obtain the theoretical results by verifying the proposed conditions. Some numerical experiments are given to validate our analysis.