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Analysis of a new stabilized higher order finite element method for advection–diffusion equations
Ist Teil von
Computer methods in applied mechanics and engineering, 2006-12, Vol.196 (1), p.538-550
Ort / Verlag
Amsterdam: Elsevier B.V
Erscheinungsjahr
2006
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
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
⩾
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
⩾
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.