Superconvergent Finite Element Method on A Shishkin Mesh for Convection-Di usion Problems
نویسنده
چکیده
In this work, the bilinear nite element method on a Shishkin mesh for convection-diiusion problems is analyzed in the two-dimensional setting. A su-perconvergent rate N ?2 ln 2 N + N ?3=2 is established on a discrete energy norm. This rate is uniformly valid with respect to the singular perturbation parameter. As a by-product, an-uniform convergence of the same order is obtained for the L 2-norm. L 1 norm is proved for some mesh points in the boundary layer region.
منابع مشابه
Superconvergent Finite Element Methods on A Shishkin Mesh for Convection-Di usion Problems
In this work, the bilinear nite element method on a Shishkin mesh for convection-diiusion problems is analyzed in the two-dimensional setting. A su-perconvergent rate O(N ?2 ln 2 N + N ?3=2) in a discrete-weighted energy norm is established under certain regularity assumption. This convergent rate is uniformly valid with respect to the singular perturbation parameter. Numerical tests indicate t...
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