Analysis of the SDFEM for singularly perturbed differential-difference equations

作者：Liu, Li-Bin^*; Leng, Haitao; Long, Guangqing

来源：Calcolo, 2018, 55(3): 23.

DOI：10.1007/s10092-018-0265-4

• Streamline diffusion finite element method
• Singularly perturbed
• Monitor function
• Green function
• Bakhvalov mesh

In this paper, the stability and accuracy of a streamline diffusion finite element method (SDFEM) for the singularly perturbed differential-difference equation of convection term with a small shift is considered. With a special choice of the stabilization quadratic bubble function and by using the discrete Green's function, the new method is shown to have an optimal second order in the sense that , where is the SDFEM approximation of the exact solution u in linear finite element space . At last, a second order uniform convergence result for the SDFEM is obtained. Numerical results are given to confirm the -uniform convergence rate of the nodal errors.

• 出版日期2018-9
• 单位南宁师范大学