We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special structure of the stiffness matrix that allows us to extend the diagonal Pade'\ approximation to solve ordinary differential equations with source terms. The unconditional stability, hp error estimates, and hp superconvergence at the nodes of the continuous time Galerkin method are proved. Numerical examples confirm our theoretical results.

Publication:

SIAM Journal on Scientific Computing Volume 46, Issue 3 Jun 2024

http://dx.doi.org/10.1137/23M1572787

Author:

Zhiming Chen

LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science and School of Mathematical Science, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

Email: zmchen@lsec.cc.ac.cn

Yong Liu

LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

Email: yongliu@lsec.cc.ac.cn