On the relationship of local projection stabilization to other stabilized methods for one-dimensional advection–diffusion equations
On the relationship of local projection stabilization to other stabilized methods for one-dimensional advection–diffusion equations
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DOI：
10.1016/j.cma.2008.10.016
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发表时间：
2009-01
影响因子：
7.2
通讯作者：
L. Tobiska
中科院分区：
文献类型：
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作者：
L. Tobiska
本文研究了求解奇异摄动对流扩散两点边值问题的局部投影稳定化（LPS）的一层方法。消除丰富，我们最终与微分残差方法（DRM），符合分段线性与流线迎风彼得罗夫-伽辽金（SUPG）方法和分段多项式的次数r 2与变分多尺度方法（VMS）。此外，我们表明，在某些情况下，稳定参数可以选择这样一种方式，分段线性部分的解决方案成为节点精确。通过这种方式，我们得到了稳定化参数依赖于局部网格大小，近似空间的多项式次数r和问题的数据的显式公式。最后，我们讨论了不同模式的离散解决方案时，改变稳定参数的行为。
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⩾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.