Published

An optimal streamline diffusion finite element method for a singularly perturbed problem

Long Chen and Jinchao Xu.

In AMS Contemporary Mathematics Series: Recent Advances in Adaptive Computation, volume 383, pages 236-246, Hangzhou, 2005

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ABSTRACT:

 
The stability and accuracy of a streamline
diffusion finite element method (SDFEM) on arbitrary grids applied to
a linear 1-d singularly perturbed problem are studied in this
paper. With a special choice of the stabilization quadratic bubble
function, the SDFEM is shown to have an optimal second order in the
sense that u − uh ≤ C inf vh ∈V h u − vh, where uh is the
SDFEM approximation of the exact solution u and Vh is the linear
finite element space. With the quasi-optimal interpolation error
estimate, quasi-optimal convergence results for the SDFEM are
obtained. As a conse- quence, an open question about the optimal
choice of the monitor function for a second order scheme in the moving
mesh method is answered.