Analysis of the SDFEM in a streamline diffusion norm for singularly perturbed convection diffusion problems

Abstract In this paper we analyze a streamline diffusion finite element method (SDFEM) for a model singularly perturbed convection diffusion problem. By decreasing the standard stabilization parameter properly near the exponential layers, we obtain uniform estimates in a new norm which is stronger than the usual e -energy norm and weaker than the standard streamline diffusion norm. Through the analysis we know about the influences of the stabilization parameter on the SDFEM solutions.

[1]  R. Bruce Kellogg,et al.  Corner singularities and boundary layers in a simple convection–diffusion problem☆ , 2005 .

[2]  Martin Stynes,et al.  A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem☆ , 1997 .

[3]  Xiaowei Liu,et al.  Convergence in L2 norm of the SDFEM on a Shishkin triangular mesh for problems with characteristic layers , 2016, Appl. Math. Comput..

[4]  Torsten Linß,et al.  Superconvergence analysis of the SDFEM for elliptic problems with characteristic layers , 2008 .

[5]  Lutz Tobiska,et al.  The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy , 2003, SIAM J. Numer. Anal..

[6]  Torsten Linß,et al.  Asymptotic Analysis and Shishkin-Type Decomposition for an Elliptic Convection–Diffusion Problem , 2001 .

[7]  Martin Stynes,et al.  Steady-state convection-diffusion problems , 2005, Acta Numerica.

[8]  Xiaowei Liu,et al.  Analysis of the SDFEM for convection-diffusion problems with characteristic layers , 2015, Appl. Math. Comput..

[9]  U MartinStynes.  A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem , 1997 .

[10]  H. Dai,et al.  Global GPBiCG method for complex non-Hermitian linear systems with multiple right-hand sides , 2016 .

[11]  R. Bruce Kellogg,et al.  Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem , 2007, Appl. Math. Lett..

[12]  Zhimin Zhang,et al.  Finite element superconvergence on Shishkin mesh for 2-D convection-diffusion problems , 2003, Math. Comput..