TY - JOUR
T1 - The Two-Level Local Projection Stabilization as an Enriched One-Level Approach. A One-Dimensional Study
AU - L. Tobiska & C. Winkel
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 520
EP - 534
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/735.html
KW - Local projection stabilization, finite elements, Shishkin mesh, convection diffusion equation.
AB - <p style="text-align: justify;">The two-level local projection stabilization is considered as a one-level
approach in which the enrichments on each element are piecewise polynomial
functions. The dimension of the enrichment space can be significantly
reduced without losing the convergence order. For example, using continuous
piecewise polynomials of degree $r \geq 1$, only one function per cell is needed as
enrichment instead of $r$ in the two-level approach. Moreover, in the constant
coefficient case, we derive formulas for the user-chosen stabilization parameter
which guarantee that the linear part of the solution becomes nodally exact.</p>