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Analysis of a new stabilized higher order finite element method for advection–diffusion equations

✍ Scribed by Lutz Tobiska

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
283 KB
Volume
196
Category
Article
ISSN
0045-7825

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✦ Synopsis

We consider a singularly perturbed advection-diffusion two-point boundary value problem whose solution has a single boundary layer. Based on piecewise polynomial approximations of degree k P 1, a new stabilized finite element method is derived in the framework of a variation multiscale approach. The method coincides with the SUPG method for k = 1 but differs from it for k P 2. Estimates for the error to an appropriate interpolant are given in several norms on different types of meshes. For k = 1 enhanced accuracy is achieved by superconvergence. Postprocessing guarantees the same estimates for the error to the solution itself.

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