In this paper,we first present the optimal error estimates of the semi-discrete ultra-weak discontinuous Galerkin method for solving one-dimensional linear convection-diffusion equations.Then,coupling with a kind of R...In this paper,we first present the optimal error estimates of the semi-discrete ultra-weak discontinuous Galerkin method for solving one-dimensional linear convection-diffusion equations.Then,coupling with a kind of Runge-Kutta type implicit-explicit time discretization which treats the convection term explicitly and the diffusion term implicitly,we analyze the stability and error estimates of the corresponding fully discrete schemes.The fully discrete schemes are proved to be stable if the time-stepτ≤τ0,whereτ0 is a constant independent of the mesh-size h.Furthermore,by the aid of a special projection and a careful estimate for the convection term,the optimal error estimate is also obtained for the third order fully discrete scheme.Numerical experiments are displayed to verify the theoretical results.展开更多
基金Research sponsored by NSFC grants 11871428 and 12071214Nature Science Research Program for Colleges and Universities of Jiangsu Province grant 20KJB110011+1 种基金Research is supported in part by NSFC grants U1930402the fellowship of China Postdoctoral Science Foundation(No.2020TQ0030).
文摘In this paper,we first present the optimal error estimates of the semi-discrete ultra-weak discontinuous Galerkin method for solving one-dimensional linear convection-diffusion equations.Then,coupling with a kind of Runge-Kutta type implicit-explicit time discretization which treats the convection term explicitly and the diffusion term implicitly,we analyze the stability and error estimates of the corresponding fully discrete schemes.The fully discrete schemes are proved to be stable if the time-stepτ≤τ0,whereτ0 is a constant independent of the mesh-size h.Furthermore,by the aid of a special projection and a careful estimate for the convection term,the optimal error estimate is also obtained for the third order fully discrete scheme.Numerical experiments are displayed to verify the theoretical results.
