Article ID Journal Published Year Pages File Type
499320 Computer Methods in Applied Mechanics and Engineering 2009 7 Pages PDF
Abstract

We consider the one-level approach of the local projection stabilization (LPS) for solving a singularly perturbed advection–diffusion two-point boundary value problem. Eliminating the enrichments we end up with the differentiated residual method (DRM) which coincides for piecewise linears with the streamline upwind Petrov–Galerkin (SUPG) method and for piecewise polynomials of degree r⩾2r⩾2 with the variational multiscale method (VMS). Furthermore, we show that in certain cases the stabilization parameter can be chosen in such a way that the piecewise linear part of the solution becomes nodal exact. In this way, we obtain explicit formulas for the stabilization parameter depending on the local meshsize, the polynomial degree r of the approximation space, and the data of the problem. Finally, we discuss the behaviour of different modes of the discrete solution when varying the stabilization parameter.

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Physical Sciences and Engineering Computer Science Computer Science Applications
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