Abstract In this paper, a higher order uniform convergence of the SIPG method for 1-d singularly perturbed problem of convection-diffusion type is analyzed on Shishkin mesh. A uniform error estimate of $\mathcal{O}((N^{-1}\ln N)^k)$ is obtained in energy norm, if $k$-th ($k\geq 1$) piecewise polynomial is used and the total number of element is $N$. The numerical experiments verify the theoretical results.
ZHU Peng, YANG Yu-bo, YIN Yun-hui. Higher order uniform convergent SIPG method for singularly perturbed problem. Applied Mathematics A Journal of Chinese Universities, 2014, 29(2): 233-244.
