Published

Stability of a Streamline Diffusion Finite Element Method for Turning Point Problems

Long Chen, Yonggang Wang and Jinbiao Wu

Accepted by Journal of Computational and Applied Mathematics

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Abstract:

  A one-dimensional singularly perturbed problem with a boundary
  turning point is considered in this paper. Let $V_h$ be the liner
  finite element space on a suitable grid $\mathcal T_h$. A variant of
  streamline diffusion finite element methods is proved to be almost
  uniform stable in the sense that the numerical approximation $u_h$
  satisfies $ \|u-u_h\|_{\infty}\leq C |\ln \varepsilon|$ $ \inf
  _{v_h\in V^h}\|u-v_h\|_{\infty}, $ where $C$ independent with the
  small diffusion coefficient $\varepsilon$ and the mesh $\mathcal
  T_h$. Such stability result is applied to layer-adapted grids to
  obtain almost $\varepsilon$-uniform second order scheme for turning
  point problems.